Finite Group DatabasebetaFinite Group Databasebeta| order | 528 |
| isoclinism | isoclinic class of Dic22 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C22 |
| direct product | C2×C3×Dic22 |
| unambiguous semidirect product | (C2×C11)⋊(C3×Q8) |
| Hall | C3×C11 ⋊ C2×Q8 |
| Sylow | C11 ⋊ C2×C3×Q8 |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 528 |
150 conjugacy classes — view the full character table.
| maximal subgroup of | #11760498, #11760507, #11760508, … |
| maximal normal subgroup of | #11760498, #11760507, #11760508, … |
| maximal quotient of | C3×C4×Dic22, C3×#66922, C3×#66923, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(528, 126);