Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C27×C4 |
| direct product | D3×#3184 |
| Fitting | C3×#3184 ⋊ C2 |
| Sylow | C3 ⋊ C2×#3184 |
2514 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
96 conjugacy classes — view the full character table.
| maximal subgroup of | C3⋊D3×#3184, D3×#19745, D3×#33688, … |
| maximal normal subgroup of | D3×#19745, D3×#33688, D3×#61451, … |
| maximal quotient of | C3⋊D3×#3184, C2×D3×#3184, D3×#21690, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1039526);