Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
| direct product | Q8×#914 |
| Fitting | C3×Q8×SD16 ⋊ C2 |
| Sylow | C3 ⋊ Q8×AGL(1,ℤ/8) |
2010 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
90 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1050147);