Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23 |
| direct product | C3×#70885 |
| Fitting | C32×C4×D8 ⋊ C2 |
| Sylow | C32 ⋊ #2177 |
411 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
180 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10707070, #72222621, #72222642 |
| maximal normal subgroup of | C3×#10707070, #72222621, #72222642 |
| maximal quotient of | C3×#10715810 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 31816);