Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C4 · Schur multiplier (H2) = C215 |
| direct product | C23×D4×Dic3 |
| Sylow | C3 ⋊ C23×C4×D4 |
19998 conjugacy classes of subgroups.
| transitive degree | μt(G) = 384 |
240 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1076133);