Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C3 |
| direct product | C2×#10589360 |
| Sylow | C32 ⋊ C2×#365 |
456 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
144 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C3⋊D3×#365, C2×#11797953, C2×#11797962, … |
| maximal normal subgroup of | C2×C3⋊D3×#365, C2×#11797953, C2×#11797962, … |
| maximal quotient of | C2×#11772176 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 31106);