Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C2×D3×#914 |
| Fitting | C2×C32×SD16 ⋊ C22 |
| Sylow | C32 ⋊ C22×AGL(1,ℤ/8) |
3589 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
108 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D32×AGL(1,ℤ/8), D3×#81761, D3×#81845, … |
| maximal normal subgroup of | C2×D32×AGL(1,ℤ/8), D3×#81761, D3×#81845 |
| maximal quotient of | D3×#81761, C2×C3⋊D3×#914 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 152666);