Finite Group DatabasebetaFinite Group Databasebeta| order | 1056 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | D11×#217 |
| Hall | C3×C11 ⋊ C2×C22⋊C4 |
| Sylow | C11 ⋊ C2×#217 |
| Sylow | C3 ⋊ C22⋊C4×D11 |
264 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 84 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 264 |
126 conjugacy classes — view the full character table.
| maximal subgroup of | #217×AGL(1,𝔽11), D3×C22⋊C4×D11, D11×#953, … |
| maximal normal subgroup of | #217×AGL(1,𝔽11), D3×C22⋊C4×D11, D11×#953, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1056, 530);