Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C3×#1790 ⋊ C2 |
| Sylow | C3 ⋊ #24405 |
1698 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^8,3|a^2=fh,b^a=be,c^a=cf,d^a=de,e^a=eh,i^a=i^2,c^b=cg,f^b=fh,i^b=i^2,e^c=eh,f^d=fh75 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 206922);