Finite Group DatabasebetaFinite Group Databasebeta| order | 528 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | D3×C22⋊D11 |
| Fitting | C22×C3×C11 ⋊ C22 |
| Hall | C3×C11 ⋊ C2×D4 |
| Sylow | C11 ⋊ D3×D4 |
| Sylow | C3 ⋊ C2×C22⋊D11 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×D3×D11 |
| commutator, socle, cosocle | C2×C3×C11 | C23 |
| Fitting | C22×C3×C11 | C22 |
| hypercenter | C22 | D3×D11 |
| hypocenter | C3×C11 | C2×D4 |
| LCS | G ▷ C2×C3×C11 ▷ C3×C11 | |
| UCS | C1 ◁ C2 ◁ C22 | |
108 conjugacy classes of subgroups.
| transitive degree | μt(G) = 132 |
75 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#4339, #11761386, D3×D4×D11, … |
| maximal normal subgroup of | D3×#4339, #11761386, D3×D4×D11, … |
| maximal quotient of | D3×Dic11⋊C4, #11760843, #11760848, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(528, 121);