Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C28×C3 |
| direct product | C3⋊D3×#386 |
| Fitting | C32×#386 ⋊ C2 |
| Sylow | C32 ⋊ C2×#386 |
4728 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
168 conjugacy classes — view the full character table.
| maximal subgroup of | #72252266, C3⋊D3×#2403, C4×C3⋊D3×#120, … |
| maximal normal subgroup of | #72252266, C3⋊D3×#2403, C4×C3⋊D3×#120, … |
| maximal quotient of | C3⋊D3×#1889, C3⋊D3×#1437, C3⋊D3×#1438, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 35299);