Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29×C3 |
| direct product | C22×SD16×C3⋊D3 |
| Fitting | C22×C32×SD16 ⋊ C2 |
| Sylow | C32 ⋊ C23×SD16 |
5160 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
168 conjugacy classes — view the full character table.
| maximal subgroup of | C22×C3⋊D3×AGL(1,ℤ/8), C2×D3×SD16×C3⋊D3 |
| maximal normal subgroup of | C22×C3⋊D3×AGL(1,ℤ/8) |
| maximal quotient of | C2×D3×SD16×C3⋊D3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 152558);