Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C23×C4 |
| direct product | C3×D3×#498 |
| Fitting | C32×#498 ⋊ C2 |
| Sylow | C32 ⋊ C2×#498 |
897 conjugacy classes of subgroups.
| transitive degree | μt(G) = 384 |
198 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D3×#1715, C3×D3×#3184, C3×D3×#1705, … |
| maximal normal subgroup of | C3×D3×#1715, C3×D3×#3184, C3×D3×#1705 |
| maximal quotient of | AGL(1,ℤ/9)×#498 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 108885);