Finite Group DatabasebetaFinite Group Databasebeta| order | 1056 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | D3×(C2×D11)⋊C4 |
| Fitting | C2×C3×C4×C11 ⋊ C22 |
| Hall | C3×C11 ⋊ C2×C22⋊C4 |
| Sylow | C11 ⋊ D3×C22⋊C4 |
| Sylow | C3 ⋊ C2×(C2×D11)⋊C4 |
264 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 74 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 264 |
150 conjugacy classes — view the full character table.
| maximal subgroup of | D3×((C2×D11)⋊C4)⋊C5, D3×C22⋊C4×D11, D3×#66935, … |
| maximal normal subgroup of | D3×((C2×D11)⋊C4)⋊C5, D3×C22⋊C4×D11, D3×#66935, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1056, 459);