Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C25 |
| direct product | C3×#69662 |
| Fitting | C32×#390 ⋊ C2 |
| Sylow | C32 ⋊ #1792 |
1369 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
180 conjugacy classes — view the full character table.
| maximal subgroup of | #72252271, #72252275, C3×#10943884, … |
| maximal normal subgroup of | #72252271, #72252275, C3×#10943884, … |
| maximal quotient of | C3×#10686697, C3×#10687314 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 18865);