Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C24×C4 |
| direct product | C3×D3×#486 |
| Fitting | C32×#486 ⋊ C2 |
| Sylow | C32 ⋊ C2×#486 |
1115 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
198 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D3×#1715, C3×D3×#1721, C3×D3×#3184, … |
| maximal normal subgroup of | C3×D3×#1715, C3×D3×#1721, C3×D3×#3184 |
| maximal quotient of | AGL(1,ℤ/9)×#486 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 107360);