Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C42 · Schur multiplier (H2) = C212 |
| direct product | C22×D3×#95 |
| Fitting | C22×C3×#95 ⋊ C2 |
| Sylow | C3 ⋊ C23×#95 |
14334 conjugacy classes of subgroups.
| transitive degree | μt(G) = 384 |
240 conjugacy classes — view the full character table.
| maximal subgroup of | C22×D3×#392, D3×#8020, C2×D3×#1438, … |
| maximal normal subgroup of | C22×D3×#392, D3×#8020, C2×D3×#1438, … |
| maximal quotient of | D3×#20354, D3×D4×#95 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 327734);