Finite Group DatabasebetaFinite Group Databasebeta| order | 792 |
| isoclinism | isoclinic class of Dic6 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C11 · Schur multiplier (H2) = C2 |
| direct product | C3×C11×#67 |
| Fitting | C22×C32×C11 ⋊ C2 |
| Hall | C32×C11 ⋊ D4 |
| Sylow | C32 ⋊ D4×C11 |
74 conjugacy classes of subgroups.
| transitive degree | μt(G) = 132 |
297 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×#10587242, C3×#10587244, C3×D11×#67, … |
| maximal normal subgroup of | C3×#10587242, C3×#10587244, C3×D11×#67, … |
| maximal quotient of | C3×C11×Dic3⋊C4, C3×C11×(C2×D3)⋊C4, C3×C11×#213, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(792, 89);