Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
| direct product | D3×#3114 |
| Fitting | C3×#3114 ⋊ C2 |
| Sylow | C3 ⋊ C2×#3114 |
2582 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
96 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#61454, D3×#60558, D3×#60574, … |
| maximal normal subgroup of | D3×#61451, D3×#61454, D3×#60558, … |
| maximal quotient of | D3×#21452, D3×#20739 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1037674);