Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C3 · Schur multiplier (H2) = C210 |
| direct product | C22×C3×D3×D8 |
| Fitting | C22×C32×D8 ⋊ C2 |
| Sylow | C32 ⋊ C23×D8 |
4121 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
252 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C3×D3×#442 |
| maximal normal subgroup of | C2×C3×D3×#442 |
| maximal quotient of | C3×#11701722 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 152541);