Finite Group DatabasebetaFinite Group Databasebeta| order | 528 |
| isoclinism | isoclinic class of A4×D11 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C22 |
| direct product | C2×A4×D11 |
| unambiguous semidirect product | C11⋊(C22×A4) |
| unambiguous semidirect product | (C2×C11)⋊(C2×A4) |
| unambiguous semidirect product | (C23×D11)⋊C3 |
| Fitting, socle | C23×C11 ⋊ C2×C3 |
| derived | C22×C11 ⋊ C22×C3 |
| Hall | C23×D11 ⋊ C3 |
| Sylow | C11 ⋊ C22×A4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | A4×D11 |
| commutator, cosocle, hypocenter | C22×C11 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C23×C11 | C2×C3 |
| LCS | G ▷ C22×C11 | |
| UCS | C1 ◁ C2 | |
78 conjugacy classes of subgroups.
| transitive degree | μt(G) = 66 |
56 conjugacy classes — view the full character table.
| maximal subgroup of | D11×SL(2,ℤ/4), #11761330, #11761331, … |
| maximal normal subgroup of | D11×SL(2,ℤ/4), #11761330, #11761331, … |
| maximal quotient of | A4×Dic22, C4×A4×D11, A4×D44, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(528, 163);