Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C25 |
| direct product | C2×C3×#5147 |
| Fitting | C22×C32×D8 ⋊ C2 |
| Sylow | C32 ⋊ C2×#509 |
969 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
180 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#11701722, #72222779, C3×#10948665, … |
| maximal normal subgroup of | C3×#11701722, #72222779, C3×#10948665, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 133554);