Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | D8×ΓL(1,𝔽25) |
| Fitting | C3×C8×D8 ⋊ C2 |
| Sylow | C3 ⋊ M16×D8 |
794 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
126 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 140985);