Finite Group DatabasebetaFinite Group Databasebeta| order | 1056 |
| isoclinism | isoclinic class of D3×D11 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C4 |
| direct product | Dic3×C11⋊C8 |
| derived, Hall | C3×C11 ⋊ C4×C8 |
| Sylow | C11 ⋊ C8×Dic3 |
| Sylow | C3 ⋊ C4×C11⋊C8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2×C4 | D3×D11 |
| commutator, hypocenter | C3×C11 | C4×C8 |
| Fitting, cosocle | C2×C3×C4×C11 | C22 |
| socle, prime radical | C22×C3×C11 | C2×C4 |
| LCS | G ▷ C3×C11 | |
| UCS | C1 ◁ C2×C4 | |
88 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1056 |
168 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1056, 24);