Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | D3×#2190 |
| Fitting | C3×#2190 ⋊ C2 |
| Sylow | C3 ⋊ C2×#2190 |
1180 conjugacy classes of subgroups.
| transitive degree | μt(G) = 48 |
60 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#33688, #72219792, D3×#33692, … |
| maximal normal subgroup of | D3×#33688, D3×#33692, D3×#33691, … |
| maximal quotient of | #72219792, D3×#13025 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 323449);