| order | 768 |
| isoclinism | isoclinic class of Dic6 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C42 · Schur multiplier (H2) = C28×C4 |
| direct product | C2×C4×#901 |
| Fitting | C22×C3×C4×C8 ⋊ C2 |
| Sylow | C3 ⋊ C2×C4×#131 |
3366 conjugacy classes of subgroups.
| transitive degree | μt(G) = 384 |
288 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1032969);