Finite Group DatabasebetaFinite Group Databasebeta| order | 1056 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | SL(2,𝔽3)×Dic11 |
| unambiguous semidirect product | C11⋊(C4×SL(2,𝔽3)) |
| unambiguous semidirect product | (Q8×Dic11)⋊C3 |
| derived | Q8×C11 ⋊ C3×C4 |
| Hall | Q8×Dic11 ⋊ C3 |
| Sylow | C11 ⋊ C4×SL(2,𝔽3) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C22 | A4×D11 |
| commutator, hypocenter | Q8×C11 | C3×C4 |
| Fitting, cosocle | C2×Q8×C11 | C2×C3 |
| socle | C22×C11 | C2×A4 |
| prime radical | C2×C11×SL(2,𝔽3) | C2 |
| LCS | G ▷ Q8×C11 | |
| UCS | C1 ◁ C22 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 352 |
98 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1056, 227);