Finite Group DatabasebetaFinite Group Databasebeta| order | 528 |
| isoclinism | isoclinic class of D11×S4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C22 |
| direct product | D11×S4 |
| unambiguous semidirect product | (C11×S4)⋊C2 |
| unambiguous semidirect product | (C11⋊S4)⋊C2 |
| unambiguous semidirect product | (A4×D11)⋊C2 |
| Fitting, socle | C22×C11 ⋊ C2×D3 |
| derived | C11×A4 ⋊ C22 |
| Sylow | C11 ⋊ C2×S4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C11×A4 | C22 |
| Fitting, socle | C22×C11 | C2×D3 |
| LCS | G ▷ C11×A4 | |
| UCS | C1 | |
66 conjugacy classes of subgroups.
| minimal degree | μ(G) = 15 |
| transitive degree | μt(G) = 44 |
35 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D11×S4, C3×D11×S4, D11×C3⋊S4, … |
| maximal normal subgroup of | C2×D11×S4, C3×D11×S4, S4×AGL(1,𝔽11) |
| maximal quotient of | #11761317, #11761318, #11761319, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(528, 160);