Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | C2×#68670 |
| Fitting | C2×C3×#336 ⋊ C2 |
| Sylow | C3 ⋊ C2×#1862 |
1974 conjugacy classes of subgroups.
| transitive degree | μt(G) = 384 |
156 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 170484);