Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C3 · Schur multiplier (H2) = C29 |
| direct product | C3×#87282 |
| Fitting | C2×C32×H(5,𝔽2) ⋊ C2 |
| Sylow | C32 ⋊ #3498 |
3945 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
234 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D3×#3498, C3×#11661868, #72268950 |
| maximal normal subgroup of | C3×D3×#3498, C3×#11661868 |
| maximal quotient of | #72268950 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 139950);