Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C3 |
| direct product | C2×C3⋊D3×#108 |
| Fitting | C2×C32×#108 ⋊ C2 |
| Sylow | C32 ⋊ C22×#108 |
1440 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
168 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C3⋊D3×#365, C2×C3⋊D3×#361, C2×C3⋊D3×#444, … |
| maximal normal subgroup of | C2×C3⋊D3×#365, C2×C3⋊D3×#361, C2×C3⋊D3×#444, … |
| maximal quotient of | C2×C3⋊D3×#334 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 92617);