Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C42 · Schur multiplier (H2) = C23×C4 |
| direct product | C3×C4×#806 |
| Fitting | C32×C4×C22⋊C4 ⋊ C2 |
| Sylow | C32 ⋊ C4×#99 |
953 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
252 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#10590410, C4×#10590404, C3×C4×#5032 |
| maximal normal subgroup of | C4×#10590410, C4×#10590404, C3×C4×#5032 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 17760);