Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C26×C3 |
| direct product | C2×C3⋊D3×C4⋊C8 |
| Fitting | C2×C32×C4⋊C8 ⋊ C2 |
| Sylow | C32 ⋊ C22×C4⋊C8 |
1920 conjugacy classes of subgroups.
| transitive degree | μt(G) = 576 |
240 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C3⋊D3×#334, C2×C8×D4×C3⋊D3, C2×C3⋊D3×D4⋊C8 |
| maximal normal subgroup of | C2×C3⋊D3×#334, C2×C8×D4×C3⋊D3, C2×C3⋊D3×D4⋊C8 |
| maximal quotient of | C2×C3⋊D3×#334, C2×C3⋊D3×#364 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 92221);