Finite Group DatabasebetaFinite Group Databasebeta| order | 1056 |
| isoclinism | isoclinic class of #63140 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C22×#63140 |
| Hall | C3×C11 ⋊ C22×D4 |
| Sylow | C11 ⋊ C22×#67 |
| Sylow | C3 ⋊ C22×C22⋊D11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | D3×D11 |
| commutator, cosocle | C2×C3×C11 | C24 |
| Frattini | C2 | C22×D3×D11 |
| Fitting, socle | C23×C3×C11 | C22 |
| hypocenter | C3×C11 | C22×D4 |
| LCS | G ▷ C2×C3×C11 ▷ C3×C11 | |
| UCS | C1 ◁ C23 | |
472 conjugacy classes of subgroups.
| transitive degree | μt(G) = 528 |
156 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1056, 947);