Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C3 · Schur multiplier (H2) = C29 |
| direct product | C3×D3×#532 |
| Fitting | C32×#532 ⋊ C2 |
| Sylow | C32 ⋊ C2×#532 |
3611 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
252 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D3×#3151, D32×#532, D3×#83287, … |
| maximal normal subgroup of | C3×D3×#3151, D32×#532, D3×#83287, … |
| maximal quotient of | AGL(1,ℤ/9)×#532, C3×D3×#3184 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 134748);