Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C28 |
| direct product | C4×Q8×Dic6 |
| Sylow | C3 ⋊ C4×Q82 |
2324 conjugacy classes of subgroups.
| transitive degree | μt(G) = 768 |
180 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 329572);