Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C3×#2068 ⋊ C2 |
| Sylow | C3 ⋊ #23609 |
1138 conjugacy classes of subgroups.
| transitive degree | μt(G) = 384 |
Polycyclic presentation:
2^8,3|a^2=ef,b^2=e,d^2=h,e^2=h,f^2=h,g^2=h,b^a=be,c^a=cf,e^a=eh,f^a=fh,g^a=gh,c^b=cg,i^b=i^2,e^c=eh,f^c=fh,g^c=gh,i^c=i^2,i^d=i^296 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 198184);