Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4 |
| direct product | C4×#63791 |
| Fitting | C32×C4×C8 ⋊ C22 |
| Sylow | C32 ⋊ C2×C4×M16 |
1393 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
192 conjugacy classes — view the full character table.
| maximal subgroup of | C4×D32×M16, #72243471, #72243477 |
| maximal normal subgroup of | C4×D32×M16, #72243471, #72243477 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 91164);