Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | D3×#2200 |
| Fitting | C3×#2200 ⋊ C2 |
| Sylow | C3 ⋊ C2×#2200 |
1328 conjugacy classes of subgroups.
| transitive degree | μt(G) = 48 |
51 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#73032, D3×#4626⋊C2, D3×#33553, … |
| maximal normal subgroup of | D3×#33551, D3×#33553, D3×#33550, … |
| maximal quotient of | D3×#13344, D3×#13347, D3×#13346, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 323600);