Finite Group DatabasebetaFinite Group Databasebeta| order | 528 |
| isoclinism | isoclinic class of D11 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C8 · Schur multiplier (H2) = C2 |
| direct product | C3×C8×D11 |
| Fitting | C3×C8×C11 ⋊ C2 |
| derived, Sylow | C11 ⋊ C2×C3×C8 |
| Hall | C3×C11 ⋊ C2×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C8 | D11 |
| commutator, hypocenter | C11 | C2×C3×C8 |
| Frattini | C4 | C2×C3×D11 |
| Fitting | C3×C8×C11 | C2 |
| socle | C2×C3×C11 | C2×C4 |
| prime radical | C2×C3×D11 | C4 |
| cosocle | C4×C11 | C22×C3 |
| LCS | G ▷ C11 | |
| UCS | C1 ◁ C3×C8 | |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 264 |
168 conjugacy classes — view the full character table.
| maximal subgroup of | D11×C3⋊C16, #11760471, C3×C16×D11, … |
| maximal normal subgroup of | D11×C3⋊C16, #11760471, C3×C16×D11, … |
| maximal quotient of | C3×C16×D11, C3×#66862, C3×C8×Dic11, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(528, 31);