Finite Group DatabasebetaFinite Group Databasebeta| order | 792 |
| isoclinism | isoclinic class of Dic6 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C11 · Schur multiplier (H2) = C1 |
| direct product | C3×C11×Dic6 |
| unambiguous semidirect product | C3⋊(C3×Q8×C11) |
| Hall | C32×C11 ⋊ Q8 |
| Sylow | C32 ⋊ Q8×C11 |
54 conjugacy classes of subgroups.
| transitive degree | μt(G) = 264 |
297 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×#10587144, C3×#10587149, C3×#10587150, … |
| maximal normal subgroup of | C3×#10587144, C3×#10587149, C3×#10587150, … |
| maximal quotient of | C3×C11×Dic3⋊C4, C3×C11×C4⋊Dic3, C2×C3×C11×Dic6 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(792, 85);