Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C32×#124 ⋊ C22 |
| Sylow | C32 ⋊ #3151 |
1384 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
Polycyclic presentation:
2^7,3^2|b^2=e,c^2=f,e^2=g,b^a=be,c^a=cf,e^a=eg,h^a=h^2,i^a=i^2,d^b=dg,h^b=h^2,i^b=i^2,i^c=hi^2,i^d=hi^290 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#83287, D3×#81845, #72252606 |
| maximal normal subgroup of | D3×#83287, D3×#81845, #72252606 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 108515);