Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C3×#1551 ⋊ C2 |
| Sylow | C3 ⋊ #17713 |
996 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
Polycyclic presentation:
2^8,3|a^2=f,c^2=h,d^2=g,e^2=h,f^2=gh,b^a=be,c^a=cg,e^a=eg,e^b=eh,f^b=fgh,i^d=i^296 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 137953);