Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C16 · Schur multiplier (H2) = C25 |
| direct product | D3×Q8×C16 |
| Fitting | C3×Q8×C16 ⋊ C2 |
| Sylow | C3 ⋊ C2×Q8×C16 |
582 conjugacy classes of subgroups.
| transitive degree | μt(G) = 384 |
240 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 323047);