Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4 |
| direct product | D3×#1976 |
| Fitting | C3×#1976 ⋊ C2 |
| Sylow | C3 ⋊ C2×#1976 |
1474 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
96 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#21559, D3×#13033, D3×#13030, … |
| maximal normal subgroup of | D3×#21559, D3×#13033, D3×#13030, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 173538);