Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C26×C3 |
| direct product | C8×D4×C3⋊D3 |
| Fitting | C32×C8×D4 ⋊ C2 |
| Sylow | C32 ⋊ C2×C8×D4 |
1848 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
240 conjugacy classes — view the full character table.
| maximal subgroup of | C3⋊D3×#1580, #72222657, C8×D8×C3⋊D3, … |
| maximal normal subgroup of | C3⋊D3×#1580, #72222657, C8×D8×C3⋊D3, … |
| maximal quotient of | C3⋊D3×#1580, C8×D8×C3⋊D3, C2×C8×D4×C3⋊D3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 93153);