Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25×C3 |
| direct product | C3⋊D3×#508 |
| Fitting | C32×#508 ⋊ C2 |
| Sylow | C32 ⋊ C2×#508 |
1104 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
132 conjugacy classes — view the full character table.
| maximal subgroup of | C3⋊D3×#2179, C3⋊D3×#2263, C3⋊D3×#1418 |
| maximal normal subgroup of | C3⋊D3×#2179, C3⋊D3×#2263, C3⋊D3×#1418 |
| maximal quotient of | C4×C3⋊D3×D16 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 133500);