Finite Group DatabasebetaFinite Group Databasebeta| order | 528 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | D3×Dic22 |
| unambiguous semidirect product | (D3×C11)⋊Q8 |
| Hall | C3×C11 ⋊ C2×Q8 |
| Sylow | C11 ⋊ D3×Q8 |
| Sylow | C3 ⋊ C2×Dic22 |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 264 |
75 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#4314, D3×Dic44, #11760713, … |
| maximal normal subgroup of | D3×#4314, D3×Dic44, #11760713, … |
| maximal quotient of | Dic3×Dic22, #11760741, #11760743, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(528, 99);