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- for a in [0..6] do
- > for b in [0..3] do
- > m := 2^a*3^b;
- > k := NrSmallGroups(m);
- > for i in [1..k] do
- > G := SmallGroup(m,i);
- > M := SylowSubgroup(G,2);
- > N := SylowSubgroup(G,3);
- > bool := true;
- > bool_ord := true;
- > if (IsCentral(G,M) and IdGroup(M) in [[4,2],[8,5]]) or (IsCentral(G,N) and IdGroup(N) = [27,5]) then
- > bool := false;
- > fi;
- > if bool = true and Exponent(G) in [2,3,4,6,8,12,18,24,36,72] and IsCyclic(Center(G)) then
- > if (((IsAbelian(M) and (a <= 4 or IdGroup(M) = [32,3])) and (IdGroup(M) = [16,14]) = false) or a = 3 or IdGroup(M) in [[16,3],[16,4],[16,6],[16,8], [16,11],[16,13],[32,11],[32,13],[32,24]]) or (a=6 and IdGroup(M) = [64,55]) then
- > if IdGroup(N) in [[1,1],[3,1],[9,1],[9,2],[27,3],[27,5]] then
- > Subgroups := ConjugacyClassesSubgroups(G);
- > for U in Subgroups do
- > H := Representative(U);
- > r := 1;
- > while bool = true and r <= Length(Subgroups) do
- > $41], [108,42], [144,166], [144,184], [216,136], [216,163], [432,708]] then
- > bool := false;
- > fi;
- > r := r+1;
- > od;
- > od;
- >
- > min_deg := m;
- > for chi in Irr(G) do
- > if 1 < chi[1] and chi[1] < min_deg then
- > min_deg := chi[1];
- > fi;
- > od;
- > for g in G do
- > if (Order(g) in [1,2,3,4,6,8,9,12,18]) = false then bool_ord := false; fi;
- > od;
- > if bool = true and bool_ord = true and IsAbelian(G) = false and min_deg in [2,3,4] then
- > $ Center: ", IdGroup(Center(G)), " ", StructureDescription(Center(G)), "\n");
- > counter := counter + 1;
- > fi;
- > fi;
- > fi;
- > fi;
- > od;
- > od;
- > od;
- 1 [ 27, 3 ] 3 (C3 x C3) : C3 [G,G]: [ 3, 1 ] C3 Center: [ 3, 1 ] C3
- 2 [ 6, 1 ] 6 S3 [G,G]: [ 3, 1 ] C3 Center: [ 1, 1 ] 1
- 3 [ 18, 3 ] 6 C3 x S3 [G,G]: [ 3, 1 ] C3 Center: [ 3, 1 ] C3
- 4 [ 12, 1 ] 12 C3 : C4 [G,G]: [ 3, 1 ] C3 Center: [ 2, 1 ] C2
- 5 [ 12, 3 ] 6 A4 [G,G]: [ 4, 2 ] C2 x C2 Center: [ 1, 1 ] 1
- 6 [ 12, 4 ] 6 D12 [G,G]: [ 3, 1 ] C3 Center: [ 2, 1 ] C2
- 7 [ 36, 6 ] 12 C3 x (C3 : C4) [G,G]: [ 3, 1 ] C3 Center: [ 6, 2 ] C6
- 8 [ 36, 11 ] 6 C3 x A4 [G,G]: [ 4, 2 ] C2 x C2 Center: [ 3, 1 ] C3
- 9 [ 36, 12 ] 6 C6 x S3 [G,G]: [ 3, 1 ] C3 Center: [ 6, 2 ] C6
- 10 [ 8, 3 ] 4 D8 [G,G]: [ 2, 1 ] C2 Center: [ 2, 1 ] C2
- 11 [ 8, 4 ] 4 Q8 [G,G]: [ 2, 1 ] C2 Center: [ 2, 1 ] C2
- 12 [ 24, 1 ] 24 C3 : C8 [G,G]: [ 3, 1 ] C3 Center: [ 4, 1 ] C4
- 13 [ 24, 5 ] 12 C4 x S3 [G,G]: [ 3, 1 ] C3 Center: [ 4, 1 ] C4
- 14 [ 24, 8 ] 12 (C6 x C2) : C2 [G,G]: [ 6, 2 ] C6 Center: [ 2, 1 ] C2
- 15 [ 24, 10 ] 12 C3 x D8 [G,G]: [ 2, 1 ] C2 Center: [ 6, 2 ] C6
- 16 [ 24, 11 ] 12 C3 x Q8 [G,G]: [ 2, 1 ] C2 Center: [ 6, 2 ] C6
- 17 [ 24, 12 ] 12 S4 [G,G]: [ 12, 3 ] A4 Center: [ 1, 1 ] 1
- 18 [ 72, 30 ] 12 C3 x ((C6 x C2) : C2) [G,G]: [ 6, 2 ] C6 Center: [ 6, 2 ] C6
- 19 [ 72, 42 ] 12 C3 x S4 [G,G]: [ 12, 3 ] A4 Center: [ 3, 1 ] C3
- 20 [ 16, 6 ] 8 C8 : C2 [G,G]: [ 2, 1 ] C2 Center: [ 4, 1 ] C4
- 21 [ 16, 8 ] 8 QD16 [G,G]: [ 4, 1 ] C4 Center: [ 2, 1 ] C2
- 22 [ 16, 13 ] 4 (C4 x C2) : C2 [G,G]: [ 2, 1 ] C2 Center: [ 4, 1 ] C4
- 23 [ 48, 10 ] 24 (C3 : C8) : C2 [G,G]: [ 6, 2 ] C6 Center: [ 4, 1 ] C4
- 24 [ 48, 47 ] 12 C3 x ((C4 x C2) : C2) [G,G]: [ 2, 1 ] C2 Center: [ 12, 2 ] C12
- 25 [ 32, 11 ] 8 (C4 x C4) : C2 [G,G]: [ 4, 1 ] C4 Center: [ 4, 1 ] C4
- 26 [ 96, 44 ] 24 C3 : ((C4 x C4) : C2) [G,G]: [ 12, 2 ] C12 Center: [ 4, 1 ] C4
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