Finite Group DatabasebetaFinite Group Databasebeta| order | 1056 |
| isoclinism | isoclinic class of D3×D11 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
| direct product | D11×C3⋊C16 |
| unambiguous semidirect product | (C3×D11)⋊C16 |
| derived, Hall | C3×C11 ⋊ C2×C16 |
| Sylow | C11 ⋊ C2×C3⋊C16 |
| Sylow | C3 ⋊ C16×D11 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C8 | D3×D11 |
| commutator, hypocenter | C3×C11 | C2×C16 |
| Fitting, cosocle | C3×C8×C11 | C22 |
| socle | C2×C3×C11 | C2×C8 |
| prime radical | C2×C3×D11 | C8 |
| LCS | G ▷ C3×C11 | |
| UCS | C1 ◁ C8 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 528 |
168 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1056, 5);