Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26×C3 |
| direct product | C2×#10592851 |
| Sylow | C32 ⋊ C2×#442 |
1824 conjugacy classes of subgroups.
| transitive degree | μt(G) = 576 |
156 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C3⋊D3×#442, C2×#11797956, #72222704, … |
| maximal normal subgroup of | C2×C3⋊D3×#442, C2×#11797956, #72222704, … |
| maximal quotient of | C2×#11797956, D3×#10592851, C2×#11777340 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 94160);