Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
| direct product | C2×D3×#432 |
| Fitting | C2×C3×#432 ⋊ C2 |
| Sylow | C3 ⋊ C22×#432 |
2830 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
168 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D3×#3109, D3×#20739, D3×#21379 |
| maximal normal subgroup of | C2×D3×#3109, D3×#20739, D3×#21379 |
| maximal quotient of | D3×#33426 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1033276);