Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27 |
| direct product | D3×#5032 |
| Fitting | C32×#120 ⋊ C22 |
| Sylow | C32 ⋊ C2×B(4,𝔽2) |
2135 conjugacy classes of subgroups.
| transitive degree | μt(G) = 48 |
90 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#10593244, C3×D3×#5032, D3×#10591725, … |
| maximal normal subgroup of | C3×D3×#5032, D32×B(4,𝔽2) |
| maximal quotient of | C3×D3×#5032, D3×#10591725, #72220954, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 99264);