Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C22 |
| direct product | C3×#69312 |
| Fitting | C32×#365 ⋊ C2 |
| Sylow | C32 ⋊ #2155 |
309 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
144 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10948201, #72222745, #72222756, … |
| maximal normal subgroup of | C3×#10948201, #72222745, #72222756, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 31129);