Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | D3×#5193 |
| Fitting | C32×#135 ⋊ C22 |
| Sylow | C32 ⋊ C2×#509 |
845 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
90 conjugacy classes — view the full character table.
| maximal subgroup of | D32×#509, #72222759, D3×#69249, … |
| maximal normal subgroup of | D32×#509, #72222759, D3×#69249, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 133565);