Finite Group DatabasebetaFinite Group Databasebeta| order | 528 |
| isoclinism | isoclinic class of D33 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×C4×D33 |
| Fitting | C2×C3×C4×C11 ⋊ C2 |
| derived, Hall | C3×C11 ⋊ C22×C4 |
| Sylow | C11 ⋊ C2×C4×D3 |
| Sylow | C3 ⋊ C2×C4×D11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | D33 |
| commutator, hypocenter | C3×C11 | C22×C4 |
| Frattini | C2 | C22×D33 |
| Fitting | C2×C3×C4×C11 | C2 |
| socle | C22×C3×C11 | C22 |
| prime radical | C22×D33 | C2 |
| cosocle | C2×C3×C11 | C23 |
| LCS | G ▷ C3×C11 | |
| UCS | C1 ◁ C2×C4 | |
108 conjugacy classes of subgroups.
| transitive degree | μt(G) = 264 |
144 conjugacy classes — view the full character table.
| maximal subgroup of | #11760494, #11760640, #11760747, … |
| maximal normal subgroup of | #11760494, #11760640, #11760747, … |
| maximal quotient of | C4×Dic66, C42×D33, #11761211, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(528, 147);