Finite Group DatabasebetaFinite Group Databasebeta| order | 2304 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C32×#379 ⋊ C22 |
| Sylow | C32 ⋊ C2×#1781 |
14240 conjugacy classes of subgroups.
| transitive degree | μt(G) = 48 |
Polycyclic presentation:
2^8,3^2|a^2=h,c^2=fg,c^a=ce,c^b=cef,e^c=eh,f^c=fh,g^a=gh,g^c=gh,i^a=i^2,i^d=i^2,j^a=i^2j,j^d=j^2156 conjugacy classes — view the full character table.
| maximal subgroup of | #72252284 |
| maximal normal subgroup of | #72252284 |
| maximal quotient of | #72252338, #72252366, #72252397 |
Past the SmallGroups library coverage — no SmallGroups id. Construct it from its polycyclic presentation:
gap> F := FreeGroup(IsSyllableWordsFamily, "a", "b", "c", "d", "e", "f", "g", "h", "i", "j");;
gap> coll := SingleCollector(F, [2, 2, 2, 2, 2, 2, 2, 2, 3, 3]);;
gap> SetPower(coll, 1, F.8);;
gap> SetPower(coll, 3, F.6*F.7);;
gap> SetConjugate(coll, 3, 1, F.3*F.5);;
gap> SetConjugate(coll, 3, 2, F.3*F.5*F.6);;
gap> SetConjugate(coll, 5, 3, F.5*F.8);;
gap> SetConjugate(coll, 6, 3, F.6*F.8);;
gap> SetConjugate(coll, 7, 1, F.7*F.8);;
gap> SetConjugate(coll, 7, 3, F.7*F.8);;
gap> SetConjugate(coll, 9, 1, F.9^2);;
gap> SetConjugate(coll, 9, 4, F.9^2);;
gap> SetConjugate(coll, 10, 1, F.9^2*F.10);;
gap> SetConjugate(coll, 10, 4, F.10^2);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);