Finite Group DatabasebetaFinite Group Databasebeta| order | 1056 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | D11×#239 |
| Fitting | C3×Q8×C11 ⋊ C22 |
| Hall | C3×C11 ⋊ C2×#41 |
| Sylow | C11 ⋊ C2×#239 |
| Sylow | C3 ⋊ #41×D11 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×D3×D11 |
| commutator, socle, cosocle | C2×C3×C11 | C24 |
| Fitting | C3×Q8×C11 | C22 |
| hypercenter | Q8 | D3×D11 |
| hypocenter | C3×C11 | C2×#41 |
| LCS | G ▷ C2×C3×C11 ▷ C3×C11 | |
| UCS | C1 ◁ C2 ◁ Q8 | |
328 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 112 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 264 |
105 conjugacy classes — view the full character table.
| maximal subgroup of | #239×AGL(1,𝔽11), D11×#914, D3×#41×D11 |
| maximal normal subgroup of | #239×AGL(1,𝔽11), D11×#914, D3×#41×D11 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1056, 937);