Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4 |
| direct product | C4×D3×ΓL(1,𝔽25) |
| Fitting | C32×C4×C8 ⋊ C22 |
| Sylow | C32 ⋊ C2×C4×M16 |
1383 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
216 conjugacy classes — view the full character table.
| maximal subgroup of | C4×D32×M16, D3×#81783, D3×#81761 |
| maximal normal subgroup of | C4×D32×M16, D3×#81783, D3×#81761 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 91163);