Finite Group DatabasebetaFinite Group Databasebeta| order | 528 |
| isoclinism | isoclinic class of D11 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C26 |
| direct product | C23×C3×D11 |
| unambiguous semidirect product | C11⋊(C24×C3) |
| unambiguous semidirect product | (C2×C11)⋊(C23×C3) |
| Fitting, socle | C23×C3×C11 ⋊ C2 |
| derived, Sylow | C11 ⋊ C24×C3 |
| Hall | C3×C11 ⋊ C24 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23×C3 | D11 |
| commutator, cosocle, hypocenter | C11 | C24×C3 |
| Frattini | C1 | G |
| Fitting, socle | C23×C3×C11 | C2 |
| LCS | G ▷ C11 | |
| UCS | C1 ◁ C23×C3 | |
268 conjugacy classes of subgroups.
| transitive degree | μt(G) = 264 |
168 conjugacy classes — view the full character table.
| maximal subgroup of | C2×(C2×D11)⋊Dic3, D11×#217, #11761008, … |
| maximal normal subgroup of | C2×(C2×D11)⋊Dic3, D11×#217, #11761008, … |
| maximal quotient of | C22×C3×Dic22, C22×C3×C4×D11, C22×C3×D44, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(528, 167);