Finite Group DatabasebetaFinite Group Databasebeta| order | 528 |
| isoclinism | isoclinic class of D3×D11 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C4×D3×D11 |
| Fitting | C3×C4×C11 ⋊ C22 |
| derived, Hall | C3×C11 ⋊ C22×C4 |
| Sylow | C11 ⋊ C2×C4×D3 |
| Sylow | C3 ⋊ C2×C4×D11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | D3×D11 |
| commutator, hypocenter | C3×C11 | C22×C4 |
| Frattini | C2 | C2×D3×D11 |
| Fitting | C3×C4×C11 | C22 |
| socle, cosocle | C2×C3×C11 | C23 |
| prime radical | C2×D3×D11 | C2 |
| LCS | G ▷ C3×C11 | |
| UCS | C1 ◁ C4 | |
108 conjugacy classes of subgroups.
| transitive degree | μt(G) = 132 |
84 conjugacy classes — view the full character table.
| maximal subgroup of | D3×C8×D11, D11×ΓL(1,𝔽25), D3×#4313, … |
| maximal normal subgroup of | D3×C8×D11, D11×ΓL(1,𝔽25), D3×#4313, … |
| maximal quotient of | D3×C8×D11, D11×ΓL(1,𝔽25), D3×#4313, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(528, 106);