Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | D9×#453 |
| Fitting | C9×#453 ⋊ C2 |
| Sylow | C9 ⋊ C2×#453 |
1266 conjugacy classes of subgroups.
| transitive degree | μt(G) = 72 |
96 conjugacy classes — view the full character table.
| maximal subgroup of | #72220062, AGL(1,ℤ/9)×#453, D9×#5935, … |
| maximal normal subgroup of | AGL(1,ℤ/9)×#453, C2×D9×#453, D9×#3018, … |
| maximal quotient of | #72220062, C2×D9×#453 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 98765);