Finite Group DatabasebetaFinite Group Databasebeta| order | 1056 |
| isoclinism | isoclinic class of D11×C42⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C4 |
| direct product | D11×C42⋊C3 |
| unambiguous semidirect product | C11⋊(C2×C42⋊C3) |
| unambiguous semidirect product | (C42×D11)⋊C3 |
| Fitting, derived | C42×C11 ⋊ C2×C3 |
| Hall | C42×D11 ⋊ C3 |
| Sylow | C11 ⋊ C2×C42⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C42×C11 | C2×C3 |
| Frattini | C22 | A4×D11 |
| socle | C22×C11 | C2×A4 |
| LCS | G ▷ C42×C11 | |
| UCS | C1 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 132 |
56 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1056, 223);