Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C28 |
| direct product | #67×#95 |
| Fitting | C22×C3×#95 ⋊ C2 |
| Sylow | C3 ⋊ D4×#95 |
3562 conjugacy classes of subgroups.
| transitive degree | μt(G) = 384 |
180 conjugacy classes — view the full character table.
| maximal subgroup of | #72270967, #72270978, #72271146, … |
| maximal normal subgroup of | #72270967, #72270978, #72271146, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 91036);