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__Sign Up__- Counting the groups of finite representation type of order 2 = [ 2 ]
- Counting the groups of finite representation type of order 3 = [ 3 ]
- Counting the groups of finite representation type of order 4 = [ 2, 2 ]
- Checking it in characteristic 2
- C4
- Of finite representation type: 1
- Of infinite representation type: 1
- Counting the groups of finite representation type of order 5 = [ 5 ]
- Counting the groups of finite representation type of order 6 = [ 2, 3 ]
- Counting the groups of finite representation type of order 7 = [ 7 ]
- Counting the groups of finite representation type of order 8 = [ 2, 2, 2 ]
- Checking it in characteristic 2
- C8
- Of finite representation type: 1
- Of infinite representation type: 4
- Counting the groups of finite representation type of order 9 = [ 3, 3 ]
- Checking it in characteristic 3
- C9
- Of finite representation type: 1
- Of infinite representation type: 1
- Counting the groups of finite representation type of order 10 = [ 2, 5 ]
- Counting the groups of finite representation type of order 11 = [ 11 ]
- Counting the groups of finite representation type of order 12 = [ 2, 2, 3 ]
- Checking it in characteristic 2
- C3 : C4 C12
- Of finite representation type: 2
- Of infinite representation type: 3
- Counting the groups of finite representation type of order 13 = [ 13 ]
- Counting the groups of finite representation type of order 14 = [ 2, 7 ]
- Counting the groups of finite representation type of order 15 = [ 3, 5 ]
- Counting the groups of finite representation type of order 16 = [ 2, 2, 2, 2 ]
- Checking it in characteristic 2
- C16
- Of finite representation type: 1
- Of infinite representation type: 13
- Counting the groups of finite representation type of order 17 = [ 17 ]
- Counting the groups of finite representation type of order 18 = [ 2, 3, 3 ]
- Checking it in characteristic 3
- D18 C18
- Of finite representation type: 2
- Of infinite representation type: 3
- Counting the groups of finite representation type of order 19 = [ 19 ]
- Counting the groups of finite representation type of order 20 = [ 2, 2, 5 ]
- Checking it in characteristic 2
- C5 : C4 C20 C5 : C4
- Of finite representation type: 3
- Of infinite representation type: 2
- Counting the groups of finite representation type of order 21 = [ 3, 7 ]
- Counting the groups of finite representation type of order 22 = [ 2, 11 ]
- Counting the groups of finite representation type of order 23 = [ 23 ]
- Counting the groups of finite representation type of order 24 = [ 2, 2, 2, 3 ]
- Checking it in characteristic 2
- C3 : C8 C24
- Of finite representation type: 2
- Of infinite representation type: 13
- Counting the groups of finite representation type of order 25 = [ 5, 5 ]
- Checking it in characteristic 5
- C25
- Of finite representation type: 1
- Of infinite representation type: 1
- Counting the groups of finite representation type of order 26 = [ 2, 13 ]
- Counting the groups of finite representation type of order 27 = [ 3, 3, 3 ]
- Checking it in characteristic 3
- C27
- Of finite representation type: 1
- Of infinite representation type: 4
- Counting the groups of finite representation type of order 28 = [ 2, 2, 7 ]
- Checking it in characteristic 2
- C7 : C4 C28
- Of finite representation type: 2
- Of infinite representation type: 2
- Counting the groups of finite representation type of order 29 = [ 29 ]
- Counting the groups of finite representation type of order 30 = [ 2, 3, 5 ]
- Counting the groups of finite representation type of order 31 = [ 31 ]
- Counting the groups of finite representation type of order 32 = [ 2, 2, 2, 2, 2 ]
- Checking it in characteristic 2
- C32
- Of finite representation type: 1
- Of infinite representation type: 50
- Counting the groups of finite representation type of order 33 = [ 3, 11 ]
- Counting the groups of finite representation type of order 34 = [ 2, 17 ]
- Counting the groups of finite representation type of order 35 = [ 5, 7 ]
- Counting the groups of finite representation type of order 36 = [ 2, 2, 3, 3 ]
- Checking it in characteristic 2
- C9 : C4 C36 C3 x (C3 : C4) (C3 x C3) : C4 C12 x C3 (C3 x C3) : C4
- Of finite representation type: 6
- Of infinite representation type: 8
- Checking it in characteristic 3
- C9 : C4 C36 (C2 x C2) : C9 D36 C18 x C2
- Of finite representation type: 5
- Of infinite representation type: 9
- Counting the groups of finite representation type of order 37 = [ 37 ]
- Counting the groups of finite representation type of order 38 = [ 2, 19 ]
- Counting the groups of finite representation type of order 39 = [ 3, 13 ]
- Counting the groups of finite representation type of order 40 = [ 2, 2, 2, 5 ]
- Checking it in characteristic 2
- C5 : C8 C40 C5 : C8
- Of finite representation type: 3
- Of infinite representation type: 11
- Counting the groups of finite representation type of order 41 = [ 41 ]
- Counting the groups of finite representation type of order 42 = [ 2, 3, 7 ]
- Counting the groups of finite representation type of order 43 = [ 43 ]
- Counting the groups of finite representation type of order 44 = [ 2, 2, 11 ]
- Checking it in characteristic 2
- C11 : C4 C44
- Of finite representation type: 2
- Of infinite representation type: 2
- Counting the groups of finite representation type of order 45 = [ 3, 3, 5 ]
- Checking it in characteristic 3
- C45
- Of finite representation type: 1
- Of infinite representation type: 1
- Counting the groups of finite representation type of order 46 = [ 2, 23 ]
- Counting the groups of finite representation type of order 47 = [ 47 ]
- Counting the groups of finite representation type of order 48 = [ 2, 2, 2, 2, 3 ]
- Checking it in characteristic 2
- C3 : C16 C48
- Of finite representation type: 2
- Of infinite representation type: 50
- Counting the groups of finite representation type of order 49 = [ 7, 7 ]
- Checking it in characteristic 7
- C49
- Of finite representation type: 1
- Of infinite representation type: 1
- Counting the groups of finite representation type of order 50 = [ 2, 5, 5 ]
- Checking it in characteristic 5
- D50 C50
- Of finite representation type: 2
- Of infinite representation type: 3
- Counting the groups of finite representation type of order 51 = [ 3, 17 ]
- Counting the groups of finite representation type of order 52 = [ 2, 2, 13 ]
- Checking it in characteristic 2
- C13 : C4 C52 C13 : C4
- Of finite representation type: 3
- Of infinite representation type: 2
- Counting the groups of finite representation type of order 53 = [ 53 ]
- Counting the groups of finite representation type of order 54 = [ 2, 3, 3, 3 ]
- Checking it in characteristic 3
- D54 C54
- Of finite representation type: 2
- Of infinite representation type: 13
- Counting the groups of finite representation type of order 55 = [ 5, 11 ]
- Counting the groups of finite representation type of order 56 = [ 2, 2, 2, 7 ]
- Checking it in characteristic 2
- C7 : C8 C56
- Of finite representation type: 2
- Of infinite representation type: 11
- Counting the groups of finite representation type of order 57 = [ 3, 19 ]
- Counting the groups of finite representation type of order 58 = [ 2, 29 ]
- Counting the groups of finite representation type of order 59 = [ 59 ]
- Counting the groups of finite representation type of order 60 = [ 2, 2, 3, 5 ]
- Checking it in characteristic 2
- C5 x (C3 : C4) C3 x (C5 : C4) C15 : C4 C60 C3 x (C5 : C4) C15 : C4
- Of finite representation type: 6
- Of infinite representation type: 7
- Counting the groups of finite representation type of order 61 = [ 61 ]
- Counting the groups of finite representation type of order 62 = [ 2, 31 ]
- Counting the groups of finite representation type of order 63 = [ 3, 3, 7 ]
- Checking it in characteristic 3
- C7 : C9 C63
- Of finite representation type: 2
- Of infinite representation type: 2
- Counting the groups of finite representation type of order 64 = [ 2, 2, 2, 2, 2, 2 ]
- Checking it in characteristic 2
- C64
- Of finite representation type: 1
- Of infinite representation type: 266
- Counting the groups of finite representation type of order 65 = [ 5, 13 ]
- Counting the groups of finite representation type of order 66 = [ 2, 3, 11 ]
- Counting the groups of finite representation type of order 67 = [ 67 ]
- Counting the groups of finite representation type of order 68 = [ 2, 2, 17 ]
- Checking it in characteristic 2
- C17 : C4 C68 C17 : C4
- Of finite representation type: 3
- Of infinite representation type: 2
- Counting the groups of finite representation type of order 69 = [ 3, 23 ]
- Counting the groups of finite representation type of order 70 = [ 2, 5, 7 ]
- Counting the groups of finite representation type of order 71 = [ 71 ]
- Counting the groups of finite representation type of order 72 = [ 2, 2, 2, 3, 3 ]
- Checking it in characteristic 2
- C9 : C8 C72 C3 x (C3 : C8) (C3 x C3) : C8 C24 x C3 (C3 x C3) : C8 (C3 x C3) : C8
- Of finite representation type: 7
- Of infinite representation type: 43
- Checking it in characteristic 3
- C9 : C8 C72 Q8 : C9 C9 : Q8 C4 x D18 D72 C2 x (C9 : C4) (C18 x C2) : C2 C36 x C2 C9 x D8 C9 x Q8 ((C2 x C2) : C9) : C2 C2 x ((C2 x C2) : C9) C2 x C2 x D18 C18 x C2 x C2
- Of finite representation type: 15
- Of infinite representation type: 35
- Counting the groups of finite representation type of order 73 = [ 73 ]
- Counting the groups of finite representation type of order 74 = [ 2, 37 ]
- Counting the groups of finite representation type of order 75 = [ 3, 5, 5 ]
- Checking it in characteristic 5
- C75
- Of finite representation type: 1
- Of infinite representation type: 2
- Counting the groups of finite representation type of order 76 = [ 2, 2, 19 ]
- Checking it in characteristic 2
- C19 : C4 C76
- Of finite representation type: 2
- Of infinite representation type: 2
- Counting the groups of finite representation type of order 77 = [ 7, 11 ]
- Counting the groups of finite representation type of order 78 = [ 2, 3, 13 ]
- Counting the groups of finite representation type of order 79 = [ 79 ]
- Counting the groups of finite representation type of order 80 = [ 2, 2, 2, 2, 5 ]
- Checking it in characteristic 2
- C5 : C16 C80 C5 : C16
- Of finite representation type: 3
- Of infinite representation type: 49
- Counting the groups of finite representation type of order 81 = [ 3, 3, 3, 3 ]
- Checking it in characteristic 3
- C81
- Of finite representation type: 1
- Of infinite representation type: 14
- Counting the groups of finite representation type of order 82 = [ 2, 41 ]
- Counting the groups of finite representation type of order 83 = [ 83 ]
- Counting the groups of finite representation type of order 84 = [ 2, 2, 3, 7 ]
- Checking it in characteristic 2
- (C7 : C4) : C3 C4 x (C7 : C3) C7 x (C3 : C4) C3 x (C7 : C4) C21 : C4 C84
- Of finite representation type: 6
- Of infinite representation type: 9
- Counting the groups of finite representation type of order 85 = [ 5, 17 ]
- Counting the groups of finite representation type of order 86 = [ 2, 43 ]
- Counting the groups of finite representation type of order 87 = [ 3, 29 ]
- Counting the groups of finite representation type of order 88 = [ 2, 2, 2, 11 ]
- Checking it in characteristic 2
- C11 : C8 C88
- Of finite representation type: 2
- Of infinite representation type: 10
- Counting the groups of finite representation type of order 89 = [ 89 ]
- Counting the groups of finite representation type of order 90 = [ 2, 3, 3, 5 ]
- Checking it in characteristic 3
- C5 x D18 C9 x D10 D90 C90
- Of finite representation type: 4
- Of infinite representation type: 6
- Counting the groups of finite representation type of order 91 = [ 7, 13 ]
- Counting the groups of finite representation type of order 92 = [ 2, 2, 23 ]
- Checking it in characteristic 2
- C23 : C4 C92
- Of finite representation type: 2
- Of infinite representation type: 2
- Counting the groups of finite representation type of order 93 = [ 3, 31 ]
- Counting the groups of finite representation type of order 94 = [ 2, 47 ]
- Counting the groups of finite representation type of order 95 = [ 5, 19 ]
- Counting the groups of finite representation type of order 96 = [ 2, 2, 2, 2, 2, 3 ]
- Checking it in characteristic 2
- C3 : C32 C96
- Of finite representation type: 2
- Of infinite representation type: 229
- Counting the groups of finite representation type of order 97 = [ 97 ]
- Counting the groups of finite representation type of order 98 = [ 2, 7, 7 ]
- Checking it in characteristic 7
- D98 C98
- Of finite representation type: 2
- Of infinite representation type: 3
- Counting the groups of finite representation type of order 99 = [ 3, 3, 11 ]
- Checking it in characteristic 3
- C99
- Of finite representation type: 1
- Of infinite representation type: 1
- Counting the groups of finite representation type of order 100 = [ 2, 2, 5, 5 ]
- Checking it in characteristic 2
- C25 : C4 C100 C25 : C4 C5 x (C5 : C4) (C5 x C5) : C4 C20 x C5 C5 x (C5 : C4) (C5 x C5) : C4 (C5 x C5) : C4 (C5 x C5) : C4
- Of finite representation type: 10
- Of infinite representation type: 6
- Checking it in characteristic 5
- C25 : C4 C100 C25 : C4 D100 C50 x C2
- Of finite representation type: 5
- Of infinite representation type: 11
- Counting the groups of finite representation type of order 101 = [ 101 ]
- Counting the groups of finite representation type of order 102 = [ 2, 3, 17 ]
- Counting the groups of finite representation type of order 103 = [ 103 ]
- Counting the groups of finite representation type of order 104 = [ 2, 2, 2, 13 ]
- Checking it in characteristic 2
- C13 : C8 C104 C13 : C8
- Of finite representation type: 3
- Of infinite representation type: 11
- Counting the groups of finite representation type of order 105 = [ 3, 5, 7 ]
- Counting the groups of finite representation type of order 106 = [ 2, 53 ]
- Counting the groups of finite representation type of order 107 = [ 107 ]
- Counting the groups of finite representation type of order 108 = [ 2, 2, 3, 3, 3 ]
- Checking it in characteristic 2
- C27 : C4 C108 C3 x (C9 : C4) C9 x (C3 : C4) ((C3 x C3) : C4) : C3 (C9 : C4) : C3 (C9 x C3) : C4 ((C3 x C3) : C3) : C4 C36 x C3 C4 x ((C3 x C3) : C3) C4 x (C9 : C3) ((C3 x C3) : C3) : C4 C3 x \
- C3 x (C3 : C4) C3 x ((C3 x C3) : C4) (C3 x C3 x C3) : C4 C12 x C3 x C3 C3 x ((C3 x C3) : C4) (C3 x C3 x C3) : C4
- Of finite representation type: 18
- Of infinite representation type: 27
- Checking it in characteristic 3
- C27 : C4 C108 (C2 x C2) : C27 D108 C54 x C2
- Of finite representation type: 5
- Of infinite representation type: 40
- Counting the groups of finite representation type of order 109 = [ 109 ]
- Counting the groups of finite representation type of order 110 = [ 2, 5, 11 ]
- Counting the groups of finite representation type of order 111 = [ 3, 37 ]
- Counting the groups of finite representation type of order 112 = [ 2, 2, 2, 2, 7 ]
- Checking it in characteristic 2
- C7 : C16 C112
- Of finite representation type: 2
- Of infinite representation type: 41
- Counting the groups of finite representation type of order 113 = [ 113 ]
- Counting the groups of finite representation type of order 114 = [ 2, 3, 19 ]
- Counting the groups of finite representation type of order 115 = [ 5, 23 ]
- Counting the groups of finite representation type of order 116 = [ 2, 2, 29 ]
- Checking it in characteristic 2
- C29 : C4 C116 C29 : C4
- Of finite representation type: 3
- Of infinite representation type: 2
- Counting the groups of finite representation type of order 117 = [ 3, 3, 13 ]
- Checking it in characteristic 3
- C13 : C9 C117
- Of finite representation type: 2
- Of infinite representation type: 2
- Counting the groups of finite representation type of order 118 = [ 2, 59 ]
- Counting the groups of finite representation type of order 119 = [ 7, 17 ]
- Counting the groups of finite representation type of order 120 = [ 2, 2, 2, 3, 5 ]
- Checking it in characteristic 2
- C5 x (C3 : C8) C3 x (C5 : C8) C15 : C8 C120 C3 x (C5 : C8) C15 : C8
- Of finite representation type: 6
- Of infinite representation type: 41
- Counting the groups of finite representation type of order 121 = [ 11, 11 ]
- Checking it in characteristic 11
- C121
- Of finite representation type: 1
- Of infinite representation type: 1
- Counting the groups of finite representation type of order 122 = [ 2, 61 ]
- Counting the groups of finite representation type of order 123 = [ 3, 41 ]
- Counting the groups of finite representation type of order 124 = [ 2, 2, 31 ]
- Checking it in characteristic 2
- C31 : C4 C124
- Of finite representation type: 2
- Of infinite representation type: 2
- Counting the groups of finite representation type of order 125 = [ 5, 5, 5 ]
- Checking it in characteristic 5
- C125
- Of finite representation type: 1
- Of infinite representation type: 4
- Counting the groups of finite representation type of order 126 = [ 2, 3, 3, 7 ]
- Checking it in characteristic 3
- (C7 : C9) : C2 C2 x (C7 : C9) C7 x D18 C9 x D14 D126 C126
- Of finite representation type: 6
- Of infinite representation type: 10
- Counting the groups of finite representation type of order 127 = [ 127 ]
- Counting the groups of finite representation type of order 128 = [ 2, 2, 2, 2, 2, 2, 2 ]
- Checking it in characteristic 2
- C128
- Of finite representation type: 1
- Of infinite representation type: 2327
- Counting the groups of finite representation type of order 129 = [ 3, 43 ]
- Counting the groups of finite representation type of order 130 = [ 2, 5, 13 ]
- Counting the groups of finite representation type of order 131 = [ 131 ]
- Counting the groups of finite representation type of order 132 = [ 2, 2, 3, 11 ]
- Checking it in characteristic 2
- C11 x (C3 : C4) C3 x (C11 : C4) C33 : C4 C132
- Of finite representation type: 4
- Of infinite representation type: 6
- Counting the groups of finite representation type of order 133 = [ 7, 19 ]
- Counting the groups of finite representation type of order 134 = [ 2, 67 ]
- Counting the groups of finite representation type of order 135 = [ 3, 3, 3, 5 ]
- Checking it in characteristic 3
- C135
- Of finite representation type: 1
- Of infinite representation type: 4
- Counting the groups of finite representation type of order 136 = [ 2, 2, 2, 17 ]
- Checking it in characteristic 2
- C17 : C8 C136 C17 : C8 C17 : C8
- Of finite representation type: 4
- Of infinite representation type: 11
- Counting the groups of finite representation type of order 137 = [ 137 ]
- Counting the groups of finite representation type of order 138 = [ 2, 3, 23 ]
- Counting the groups of finite representation type of order 139 = [ 139 ]
- Counting the groups of finite representation type of order 140 = [ 2, 2, 5, 7 ]
- Checking it in characteristic 2
- C7 x (C5 : C4) C5 x (C7 : C4) C35 : C4 C140 C7 x (C5 : C4) C35 : C4
- Of finite representation type: 6
- Of infinite representation type: 5
- Counting the groups of finite representation type of order 141 = [ 3, 47 ]
- Counting the groups of finite representation type of order 142 = [ 2, 71 ]
- Counting the groups of finite representation type of order 143 = [ 11, 13 ]
- Counting the groups of finite representation type of order 144 = [ 2, 2, 2, 2, 3, 3 ]
- Checking it in characteristic 2
- C9 : C16 C144 C3 x (C3 : C16) (C3 x C3) : C16 C48 x C3 (C3 x C3) : C16 (C3 x C3) : C16
- Of finite representation type: 7
- Of infinite representation type: 190
- Checking it in characteristic 3
- C9 : C16 C144 (C4 x C4) : C9 C9 : Q16 C8 x D18 C72 : C2 C72 : C2 D144 C2 x (C9 : C8) (C9 : C8) : C2 C4 x (C9 : C4) (C9 : C4) : C4 C36 : C4 (C36 x C2) : C2 (C9 : Q8) : C2 (C9 x D8) : C2 C9\
- : Q16 (C9 x Q8) : C2 (C2 x (C9 : C4)) : C2 C36 x C4 C9 x ((C4 x C2) : C2) C9 x (C4 : C4) C72 x C2 C9 x (C8 : C2) C9 x D16 C9 x QD16 C9 x Q16 C2 . (((C2 x C2) : C9) : C2) = (Q8 : C9) . C2 (Q8 :\
- C9) : C2 ((C2 x C2) : C9) : C4 C4 x ((C2 x C2) : C9) C2 x (Q8 : C9) (Q8 : C9) : C2 C2 x (C9 : Q8) C2 x C4 x D18 C2 x D72 (C36 x C2) : C2 D8 x D18 (C2 x (C9 : C4)) : C2 Q8 x D18 (C4 x D18) : C2\
- C2 x C2 x (C9 : C4) C2 x ((C18 x C2) : C2) C36 x C2 x C2 C18 x D8 C18 x Q8 C9 x ((C4 x C2) : C2) C2 x (((C2 x C2) : C9) : C2) C2 x C2 x ((C2 x C2) : C9) (C2 x C2 x C2 x C2) : C9 C2 x C2 x C2 x D\
- 18 C18 x C2 x C2 x C2
- Of finite representation type: 52
- Of infinite representation type: 145
- Counting the groups of finite representation type of order 145 = [ 5, 29 ]
- Counting the groups of finite representation type of order 146 = [ 2, 73 ]
- Counting the groups of finite representation type of order 147 = [ 3, 7, 7 ]
- Checking it in characteristic 7
- C49 : C3 C147
- Of finite representation type: 2
- Of infinite representation type: 4
- Counting the groups of finite representation type of order 148 = [ 2, 2, 37 ]
- Checking it in characteristic 2
- C37 : C4 C148 C37 : C4
- Of finite representation type: 3
- Of infinite representation type: 2
- Counting the groups of finite representation type of order 149 = [ 149 ]
- Counting the groups of finite representation type of order 150 = [ 2, 3, 5, 5 ]
- Checking it in characteristic 5
- C25 x S3 C3 x D50 D150 C150
- Of finite representation type: 4
- Of infinite representation type: 9
- Counting the groups of finite representation type of order 151 = [ 151 ]
- Counting the groups of finite representation type of order 152 = [ 2, 2, 2, 19 ]
- Checking it in characteristic 2
- C19 : C8 C152
- Of finite representation type: 2
- Of infinite representation type: 10
- Counting the groups of finite representation type of order 153 = [ 3, 3, 17 ]
- Checking it in characteristic 3
- C153
- Of finite representation type: 1
- Of infinite representation type: 1
- Counting the groups of finite representation type of order 154 = [ 2, 7, 11 ]
- Counting the groups of finite representation type of order 155 = [ 5, 31 ]
- Counting the groups of finite representation type of order 156 = [ 2, 2, 3, 13 ]
- Checking it in characteristic 2
- (C13 : C4) : C3 C4 x (C13 : C3) C13 x (C3 : C4) C3 x (C13 : C4) C39 : C4 C156 (C13 : C4) : C3 C3 x (C13 : C4) C39 : C4
- Of finite representation type: 9
- Of infinite representation type: 9
- Counting the groups of finite representation type of order 157 = [ 157 ]
- Counting the groups of finite representation type of order 158 = [ 2, 79 ]
- Counting the groups of finite representation type of order 159 = [ 3, 53 ]
- Counting the groups of finite representation type of order 160 = [ 2, 2, 2, 2, 2, 5 ]
- Checking it in characteristic 2
- C5 : C32 C160 C5 : C32
- Of finite representation type: 3
- Of infinite representation type: 235
- Counting the groups of finite representation type of order 161 = [ 7, 23 ]
- Counting the groups of finite representation type of order 162 = [ 2, 3, 3, 3, 3 ]
- Checking it in characteristic 3
- D162 C162
- Of finite representation type: 2
- Of infinite representation type: 53
- Counting the groups of finite representation type of order 163 = [ 163 ]
- Counting the groups of finite representation type of order 164 = [ 2, 2, 41 ]
- Checking it in characteristic 2
- C41 : C4 C164 C41 : C4
- Of finite representation type: 3
- Of infinite representation type: 2
- Counting the groups of finite representation type of order 165 = [ 3, 5, 11 ]
- Counting the groups of finite representation type of order 166 = [ 2, 83 ]
- Counting the groups of finite representation type of order 167 = [ 167 ]
- Counting the groups of finite representation type of order 168 = [ 2, 2, 2, 3, 7 ]
- Checking it in characteristic 2
- (C7 : C8) : C3 C8 x (C7 : C3) C7 x (C3 : C8) C3 x (C7 : C8) C21 : C8 C168
- Of finite representation type: 6
- Of infinite representation type: 51
- Counting the groups of finite representation type of order 169 = [ 13, 13 ]
- Checking it in characteristic 13
- C169
- Of finite representation type: 1
- Of infinite representation type: 1
- Counting the groups of finite representation type of order 170 = [ 2, 5, 17 ]
- Counting the groups of finite representation type of order 171 = [ 3, 3, 19 ]
- Checking it in characteristic 3
- C19 : C9 C171 C19 : C9
- Of finite representation type: 3
- Of infinite representation type: 2
- Counting the groups of finite representation type of order 172 = [ 2, 2, 43 ]
- Checking it in characteristic 2
- C43 : C4 C172
- Of finite representation type: 2
- Of infinite representation type: 2
- Counting the groups of finite representation type of order 173 = [ 173 ]
- Counting the groups of finite representation type of order 174 = [ 2, 3, 29 ]
- Counting the groups of finite representation type of order 175 = [ 5, 5, 7 ]
- Checking it in characteristic 5
- C175
- Of finite representation type: 1
- Of infinite representation type: 1
- Counting the groups of finite representation type of order 176 = [ 2, 2, 2, 2, 11 ]
- Checking it in characteristic 2
- C11 : C16 C176
- Of finite representation type: 2
- Of infinite representation type: 40
- Counting the groups of finite representation type of order 177 = [ 3, 59 ]
- Counting the groups of finite representation type of order 178 = [ 2, 89 ]
- Counting the groups of finite representation type of order 179 = [ 179 ]
- Counting the groups of finite representation type of order 180 = [ 2, 2, 3, 3, 5 ]
- Checking it in characteristic 2
- C5 x (C9 : C4) C9 x (C5 : C4) C45 : C4 C180 C9 x (C5 : C4) C45 : C4 C3 x C3 x (C5 : C4) C15 x (C3 : C4) C3 x (C15 : C4) C5 x ((C3 x C3) : C4) (C15 x C3) : C4 C60 x C3 C3 x C3 x (C5 : C4) C3 \
- x (C15 : C4) (C15 x C3) : C4 C5 x ((C3 x C3) : C4) (C15 x C3) : C4 (C15 x C3) : C4
- Of finite representation type: 18
- Of infinite representation type: 19
- Checking it in characteristic 3
- C5 x (C9 : C4) C9 x (C5 : C4) C45 : C4 C180 C9 x (C5 : C4) C45 : C4 D10 x D18 C5 x ((C2 x C2) : C9) C18 x D10 C10 x D18 D180 C90 x C2
- Of finite representation type: 12
- Of infinite representation type: 25
- Counting the groups of finite representation type of order 181 = [ 181 ]
- Counting the groups of finite representation type of order 182 = [ 2, 7, 13 ]
- Counting the groups of finite representation type of order 183 = [ 3, 61 ]
- Counting the groups of finite representation type of order 184 = [ 2, 2, 2, 23 ]
- Checking it in characteristic 2
- C23 : C8 C184
- Of finite representation type: 2
- Of infinite representation type: 10
- Counting the groups of finite representation type of order 185 = [ 5, 37 ]
- Counting the groups of finite representation type of order 186 = [ 2, 3, 31 ]
- Counting the groups of finite representation type of order 187 = [ 11, 17 ]
- Counting the groups of finite representation type of order 188 = [ 2, 2, 47 ]
- Checking it in characteristic 2
- C47 : C4 C188
- Of finite representation type: 2
- Of infinite representation type: 2
- Counting the groups of finite representation type of order 189 = [ 3, 3, 3, 7 ]
- Checking it in characteristic 3
- C7 : C27 C189
- Of finite representation type: 2
- Of infinite representation type: 11
- Counting the groups of finite representation type of order 190 = [ 2, 5, 19 ]
- Counting the groups of finite representation type of order 191 = [ 191 ]
- Counting the groups of finite representation type of order 192 = [ 2, 2, 2, 2, 2, 2, 3 ]
- Checking it in characteristic 2
- C3 : C64 C192
- Of finite representation type: 2
- Of infinite representation type: 1541
- Counting the groups of finite representation type of order 193 = [ 193 ]
- Counting the groups of finite representation type of order 194 = [ 2, 97 ]
- Counting the groups of finite representation type of order 195 = [ 3, 5, 13 ]
- Counting the groups of finite representation type of order 196 = [ 2, 2, 7, 7 ]
- Checking it in characteristic 2
- C49 : C4 C196 C7 x (C7 : C4) (C7 x C7) : C4 C28 x C7 (C7 x C7) : C4
- Of finite representation type: 6
- Of infinite representation type: 6
- Checking it in characteristic 7
- C49 : C4 C196 D196 C98 x C2
- Of finite representation type: 4
- Of infinite representation type: 8
- Counting the groups of finite representation type of order 197 = [ 197 ]
- Counting the groups of finite representation type of order 198 = [ 2, 3, 3, 11 ]
- Checking it in characteristic 3
- C11 x D18 C9 x D22 D198 C198
- Of finite representation type: 4
- Of infinite representation type: 6
- Counting the groups of finite representation type of order 199 = [ 199 ]
- Counting the groups of finite representation type of order 200 = [ 2, 2, 2, 5, 5 ]
- Checking it in characteristic 2
- C25 : C8 C200 C25 : C8 C5 x (C5 : C8) (C5 x C5) : C8 C40 x C5 C5 x (C5 : C8) (C5 x C5) : C8 (C5 x C5) : C8 (C5 x C5) : C8 (C5 x C5) : C8
- Of finite representation type: 11
- Of infinite representation type: 41
- Checking it in characteristic 5
- C25 : C8 C200 C25 : C8 C25 : Q8 C4 x D50 D200 C2 x (C25 : C4) (C50 x C2) : C2 C100 x C2 C25 x D8 C25 x Q8 C2 x (C25 : C4) C2 x C2 x D50 C50 x C2 x C2
- Of finite representation type: 14
- Of infinite representation type: 38
- Counting the groups of finite representation type of order 201 = [ 3, 67 ]
- Counting the groups of finite representation type of order 202 = [ 2, 101 ]
- Counting the groups of finite representation type of order 203 = [ 7, 29 ]
- Counting the groups of finite representation type of order 204 = [ 2, 2, 3, 17 ]
- Checking it in characteristic 2
- C17 x (C3 : C4) C3 x (C17 : C4) C51 : C4 C204 C3 x (C17 : C4) C51 : C4
- Of finite representation type: 6
- Of infinite representation type: 6
- Counting the groups of finite representation type of order 205 = [ 5, 41 ]
- Counting the groups of finite representation type of order 206 = [ 2, 103 ]
- Counting the groups of finite representation type of order 207 = [ 3, 3, 23 ]
- Checking it in characteristic 3
- C207
- Of finite representation type: 1
- Of infinite representation type: 1
- Counting the groups of finite representation type of order 208 = [ 2, 2, 2, 2, 13 ]
- Checking it in characteristic 2
- C13 : C16 C208 C13 : C16
- Of finite representation type: 3
- Of infinite representation type: 48
- Counting the groups of finite representation type of order 209 = [ 11, 19 ]
- Counting the groups of finite representation type of order 210 = [ 2, 3, 5, 7 ]
- Counting the groups of finite representation type of order 211 = [ 211 ]
- Counting the groups of finite representation type of order 212 = [ 2, 2, 53 ]
- Checking it in characteristic 2
- C53 : C4 C212 C53 : C4
- Of finite representation type: 3
- Of infinite representation type: 2
- Counting the groups of finite representation type of order 213 = [ 3, 71 ]
- Counting the groups of finite representation type of order 214 = [ 2, 107 ]
- Counting the groups of finite representation type of order 215 = [ 5, 43 ]
- Counting the groups of finite representation type of order 216 = [ 2, 2, 2, 3, 3, 3 ]
- Checking it in characteristic 2
- C27 : C8 C216 C3 x (C9 : C8) C9 x (C3 : C8) ((C3 x C3) : C8) : C3 (C9 : C8) : C3 (C9 x C3) : C8 ((C3 x C3) : C3) : C8 C72 x C3 C8 x ((C3 x C3) : C3) C8 x (C9 : C3) ((C3 x C3) : C3) : C8 C3 x \
- C3 x (C3 : C8) C3 x ((C3 x C3) : C8) (C3 x C3 x C3) : C8 C24 x C3 x C3 ((C3 x C3) : C3) : C8 C3 x ((C3 x C3) : C8) (C3 x C3 x C3) : C8 C3 x ((C3 x C3) : C8) (C3 x C3 x C3) : C8
- Of finite representation type: 21
- Of infinite representation type: 156
- Checking it in characteristic 3
- C27 : C8 C216 Q8 : C27 C27 : Q8 C4 x D54 D216 C2 x (C27 : C4) (C54 x C2) : C2 C108 x C2 C27 x D8 C27 x Q8 ((C2 x C2) : C27) : C2 C2 x ((C2 x C2) : C27) C2 x C2 x D54 C54 x C2 x C2
- Of finite representation type: 15
- Of infinite representation type: 162
- Counting the groups of finite representation type of order 217 = [ 7, 31 ]
- Counting the groups of finite representation type of order 218 = [ 2, 109 ]
- Counting the groups of finite representation type of order 219 = [ 3, 73 ]
- Counting the groups of finite representation type of order 220 = [ 2, 2, 5, 11 ]
- Checking it in characteristic 2
- (C11 : C5) : C4 C4 x (C11 : C5) C11 x (C5 : C4) C5 x (C11 : C4) C55 : C4 C220 C11 x (C5 : C4) C55 : C4
- Of finite representation type: 8
- Of infinite representation type: 7
- Counting the groups of finite representation type of order 221 = [ 13, 17 ]
- Counting the groups of finite representation type of order 222 = [ 2, 3, 37 ]
- Counting the groups of finite representation type of order 223 = [ 223 ]
- Counting the groups of finite representation type of order 224 = [ 2, 2, 2, 2, 2, 7 ]
- Checking it in characteristic 2
- C7 : C32 C224
- Of finite representation type: 2
- Of infinite representation type: 195
- Counting the groups of finite representation type of order 225 = [ 3, 3, 5, 5 ]
- Checking it in characteristic 3
- C225 (C5 x C5) : C9 C45 x C5
- Of finite representation type: 3
- Of infinite representation type: 3
- Checking it in characteristic 5
- C225 C75 x C3
- Of finite representation type: 2
- Of infinite representation type: 4
- Counting the groups of finite representation type of order 226 = [ 2, 113 ]
- Counting the groups of finite representation type of order 227 = [ 227 ]
- Counting the groups of finite representation type of order 228 = [ 2, 2, 3, 19 ]
- Checking it in characteristic 2
- (C19 : C4) : C3 C4 x (C19 : C3) C19 x (C3 : C4) C3 x (C19 : C4) C57 : C4 C228
- Of finite representation type: 6
- Of infinite representation type: 9
- Counting the groups of finite representation type of order 229 = [ 229 ]
- Counting the groups of finite representation type of order 230 = [ 2, 5, 23 ]
- Counting the groups of finite representation type of order 231 = [ 3, 7, 11 ]
- Counting the groups of finite representation type of order 232 = [ 2, 2, 2, 29 ]
- Checking it in characteristic 2
- C29 : C8 C232 C29 : C8
- Of finite representation type: 3
- Of infinite representation type: 11
- Counting the groups of finite representation type of order 233 = [ 233 ]
- Counting the groups of finite representation type of order 234 = [ 2, 3, 3, 13 ]
- Checking it in characteristic 3
- (C13 : C9) : C2 C2 x (C13 : C9) C13 x D18 C9 x D26 D234 C234
- Of finite representation type: 6
- Of infinite representation type: 10
- Counting the groups of finite representation type of order 235 = [ 5, 47 ]
- Counting the groups of finite representation type of order 236 = [ 2, 2, 59 ]
- Checking it in characteristic 2
- C59 : C4 C236
- Of finite representation type: 2
- Of infinite representation type: 2
- Counting the groups of finite representation type of order 237 = [ 3, 79 ]
- Counting the groups of finite representation type of order 238 = [ 2, 7, 17 ]
- Counting the groups of finite representation type of order 239 = [ 239 ]
- Counting the groups of finite representation type of order 240 = [ 2, 2, 2, 2, 3, 5 ]
- Checking it in characteristic 2
- C5 x (C3 : C16) C3 x (C5 : C16) C15 : C16 C240 C3 x (C5 : C16) C15 : C16
- Of finite representation type: 6
- Of infinite representation type: 202
- Counting the groups of finite representation type of order 241 = [ 241 ]
- Counting the groups of finite representation type of order 242 = [ 2, 11, 11 ]
- Checking it in characteristic 11
- D242 C242
- Of finite representation type: 2
- Of infinite representation type: 3
- Counting the groups of finite representation type of order 243 = [ 3, 3, 3, 3, 3 ]
- Checking it in characteristic 3
- C243
- Of finite representation type: 1
- Of infinite representation type: 66
- Counting the groups of finite representation type of order 244 = [ 2, 2, 61 ]
- Checking it in characteristic 2
- C61 : C4 C244 C61 : C4
- Of finite representation type: 3
- Of infinite representation type: 2
- Counting the groups of finite representation type of order 245 = [ 5, 7, 7 ]
- Checking it in characteristic 7
- C245
- Of finite representation type: 1
- Of infinite representation type: 1
- Counting the groups of finite representation type of order 246 = [ 2, 3, 41 ]
- Counting the groups of finite representation type of order 247 = [ 13, 19 ]
- Counting the groups of finite representation type of order 248 = [ 2, 2, 2, 31 ]
- Checking it in characteristic 2
- C31 : C8 C248
- Of finite representation type: 2
- Of infinite representation type: 10
- Counting the groups of finite representation type of order 249 = [ 3, 83 ]
- Counting the groups of finite representation type of order 250 = [ 2, 5, 5, 5 ]
- Checking it in characteristic 5
- D250 C250
- Of finite representation type: 2
- Of infinite representation type: 13
- Counting the groups of finite representation type of order 251 = [ 251 ]
- Counting the groups of finite representation type of order 252 = [ 2, 2, 3, 3, 7 ]
- Checking it in characteristic 2
- (C7 : C9) : C4 C4 x (C7 : C9) C7 x (C9 : C4) C9 x (C7 : C4) C63 : C4 C252 C3 x ((C7 : C4) : C3) (C3 : C4) x (C7 : C3) (C21 : C4) : C3 C12 x (C7 : C3) C3 x C3 x (C7 : C4) C21 x (C3 : C4) C3 x \
- (C21 : C4) C7 x ((C3 x C3) : C4) (C21 x C3) : C4 C84 x C3 C7 x ((C3 x C3) : C4) (C21 x C3) : C4
- Of finite representation type: 18
- Of infinite representation type: 28
- Checking it in characteristic 3
- (C7 : C9) : C4 C4 x (C7 : C9) C7 x (C9 : C4) C9 x (C7 : C4) C63 : C4 C252 C2 x ((C7 : C9) : C2) D14 x D18 C2 x C2 x (C7 : C9) C7 x ((C2 x C2) : C9) (C14 x C2) : C9 C18 x D14 C14 x D18 D252 \
- C126 x C2
- Of finite representation type: 15
- Of infinite representation type: 31
- Counting the groups of finite representation type of order 253 = [ 11, 23 ]
- Counting the groups of finite representation type of order 254 = [ 2, 127 ]
- Counting the groups of finite representation type of order 255 = [ 3, 5, 17 ]

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