Finite Group DatabasebetaFinite Group Databasebeta| order | 792 |
| isoclinism | isoclinic class of Dic22 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C3 |
| direct product | C32×Dic22 |
| unambiguous semidirect product | C11⋊(C32×Q8) |
| Hall | C32×C11 ⋊ Q8 |
| Sylow | C11 ⋊ C32×Q8 |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 792 |
225 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10587145, C3×#10587147, C3×#10587150, … |
| maximal normal subgroup of | C3×#10587145, C3×#10587147, C3×#10587150, … |
| maximal quotient of | C32×Dic11⋊C4, C32×C4⋊Dic11, C2×C32×Dic22 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(792, 80);