Finite Group DatabasebetaFinite Group Databasebeta| order | 528 |
| isoclinism | isoclinic class of Dic22 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | C2×C3×C22⋊D11 |
| Fitting | C23×C3×C11 ⋊ C2 |
| Hall | C3×C11 ⋊ C2×D4 |
| Sylow | C11 ⋊ C2×C3×D4 |
108 conjugacy classes of subgroups.
| transitive degree | μt(G) = 264 |
150 conjugacy classes — view the full character table.
| maximal subgroup of | #11760532, C3×#66870, #11760981, … |
| maximal normal subgroup of | #11760532, C3×#66870, #11760981, … |
| maximal quotient of | C2×C3×Dic11⋊C4, C3×#66977, C2×C3×(C2×D11)⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(528, 135);