Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | #67×C22⋊Q8 |
| Fitting | C22×C3×C22⋊Q8 ⋊ C2 |
| Sylow | C3 ⋊ D4×C22⋊Q8 |
3488 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
126 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 364889);