Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
| direct product | Q8×#904 |
| Fitting | C2×C3×C8×Q8 ⋊ C2 |
| Sylow | C3 ⋊ Q8×#135 |
1786 conjugacy classes of subgroups.
| transitive degree | μt(G) = 384 |
150 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1050037);