Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
| direct product | D9×#496 |
| Fitting | C9×#496 ⋊ C2 |
| Sylow | C9 ⋊ C2×#496 |
1002 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
96 conjugacy classes — view the full character table.
| maximal subgroup of | D9×#3151, AGL(1,ℤ/9)×#496, D9×#3288 |
| maximal normal subgroup of | D9×#3151, AGL(1,ℤ/9)×#496, D9×#3288 |
| maximal quotient of | D9×#1715, D9×#1721 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 108336);