Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | D9×#509 |
| Fitting | C9×#509 ⋊ C2 |
| Sylow | C9 ⋊ C2×#509 |
600 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
96 conjugacy classes — view the full character table.
| maximal subgroup of | D9×AGL(1,ℤ/16), AGL(1,ℤ/9)×#509 |
| maximal normal subgroup of | D9×AGL(1,ℤ/16), AGL(1,ℤ/9)×#509 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 133543);