Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C3×#1806 ⋊ C2 |
| Sylow | C3 ⋊ #22687 |
858 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
Polycyclic presentation:
2^8,3|a^2=g,c^2=f,e^2=h,g^2=h,b^a=be,c^a=cf,e^a=eh,c^b=ch,d^b=de,e^b=eh,e^d=eh,i^d=i^296 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 188018);