Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | C4×#63983 |
| Fitting | C23×C32×C4 ⋊ C22 |
| Sylow | C32 ⋊ C4×#120 |
2661 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
168 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#10595278 |
| maximal normal subgroup of | C4×#10595278 |
| maximal quotient of | C4×#10591522, C4×#10591725 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 36019);