Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C26×C4 |
| direct product | D3×#1740 |
| Fitting | C3×#1740 ⋊ C2 |
| Sylow | C3 ⋊ C2×#1740 |
2350 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
132 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#11183, D3×#11129, D3×#23443, … |
| maximal normal subgroup of | D3×#11183, D3×#11129, D3×#23443, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 166997);