Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C82 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C3 ⋊ #7137 |
266 conjugacy classes of subgroups.
| transitive degree | μt(G) = 768 |
Polycyclic presentation:
2^8,3|a^2=d,b^2=e,c^2=h,d^2=f,e^2=g,f^2=h,b^a=bc,e^a=eh,d^b=dh,i^b=i^2168 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 56397);