Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C4×#5201 |
| Fitting | C3×C4×AGL(1,ℤ/8) ⋊ C2 |
| Sylow | C3 ⋊ C4×#454 |
1390 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
108 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 175460);