Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C3×#2875 ⋊ C2 |
| Sylow | C3 ⋊ #17653 |
964 conjugacy classes of subgroups.
| transitive degree | μt(G) = 384 |
Polycyclic presentation:
2^8,3|a^2=f,b^2=g,e^2=h,f^2=g,b^a=be,e^a=eg,e^b=eh,f^b=fgh,i^b=i^2,d^c=dg129 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 137559);