Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26×C3 |
| direct product | C3⋊D3×#453 |
| Fitting | C32×#453 ⋊ C2 |
| Sylow | C32 ⋊ C2×#453 |
2532 conjugacy classes of subgroups.
| transitive degree | μt(G) = 72 |
96 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C3⋊D3×#453, #72214885, #72214930, … |
| maximal normal subgroup of | C2×C3⋊D3×#453, #72214885, #72214930, … |
| maximal quotient of | C2×C3⋊D3×#453, #72220381 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 98766);