| order | 1656 |
| isoclinism | isoclinic class of Dic6 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C23 · Schur multiplier (H2) = C1 |
| direct product | C3×C23×Dic6 |
| unambiguous semidirect product | C3⋊(C3×Q8×C23) |
| Hall | C32×C23 ⋊ Q8 |
| Sylow | C32 ⋊ Q8×C23 |
54 conjugacy classes of subgroups.
| transitive degree | μt(G) = 552 |
621 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1656, 85);