Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C64 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | (C2×D3)⋊C64 |
| Fitting | C2×C3×C64 ⋊ C2 |
| Sylow | C3 ⋊ C22⋊C64 |
98 conjugacy classes of subgroups.
| transitive degree | μt(G) = 384 |
Polycyclic presentation:
2^8,3|a^2=d,d^2=e,e^2=f,f^2=g,g^2=h,b^a=bc,i^b=i^2288 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 57376);