Finite Group DatabasebetaFinite Group Databasebeta| order | 528 |
| isoclinism | isoclinic class of D3×D11 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C22×D3×D11 |
| unambiguous semidirect product | (D3×C11)⋊C23 |
| unambiguous semidirect product | (C3×D11)⋊C23 |
| unambiguous semidirect product | D33⋊C23 |
| Fitting, socle | C22×C3×C11 ⋊ C22 |
| derived, Hall | C3×C11 ⋊ C24 |
| Sylow | C11 ⋊ C23×D3 |
| Sylow | C3 ⋊ C23×D11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | D3×D11 |
| commutator, cosocle, hypocenter | C3×C11 | C24 |
| Frattini | C1 | G |
| Fitting, socle | C22×C3×C11 | C22 |
| LCS | G ▷ C3×C11 | |
| UCS | C1 ◁ C22 | |
268 conjugacy classes of subgroups.
| transitive degree | μt(G) = 132 |
84 conjugacy classes — view the full character table.
| maximal subgroup of | D11×(C2×D3)⋊C4, D3×(C2×D11)⋊C4, #11760923, … |
| maximal normal subgroup of | D11×(C2×D3)⋊C4, D3×(C2×D11)⋊C4, #11760923, … |
| maximal quotient of | C2×D11×Dic6, C2×#10587227, C2×#10587228, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(528, 164);