Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C27×C4 |
| direct product | C22×#4855 |
| Sylow | C3 ⋊ C22×#498 |
2398 conjugacy classes of subgroups.
| transitive degree | μt(G) = 768 |
144 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1039156);