Finite Group DatabasebetaFinite Group Databasebeta| order | 528 |
| isoclinism | isoclinic class of D3×D11 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| direct product | D11×C3⋊C8 |
| unambiguous semidirect product | (C3×D11)⋊C8 |
| derived, Hall | C3×C11 ⋊ C2×C8 |
| Sylow | C11 ⋊ C2×C3⋊C8 |
| Sylow | C3 ⋊ C8×D11 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4 | D3×D11 |
| commutator, hypocenter | C3×C11 | C2×C8 |
| Fitting, cosocle | C3×C4×C11 | C22 |
| socle | C2×C3×C11 | C2×C4 |
| prime radical | C2×C3×D11 | C4 |
| LCS | G ▷ C3×C11 | |
| UCS | C1 ◁ C4 | |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 264 |
84 conjugacy classes — view the full character table.
| maximal subgroup of | D3×C8×D11, D11×ΓL(1,𝔽25), #11760717, … |
| maximal normal subgroup of | D3×C8×D11, D11×ΓL(1,𝔽25), #11760717, … |
| maximal quotient of | D11×C3⋊C16, #11760471, C3⋊C8×Dic11, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(528, 5);