Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C3×#1275 ⋊ C2 |
| Sylow | C3 ⋊ #9090 |
512 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
Polycyclic presentation:
2^8,3|a^2=f,b^2=dfg,c^2=g,d^2=g,e^2=g,f^2=h,b^a=bd,c^a=ce,d^a=dg,i^a=i^2,e^b=eg,d^c=dg,e^c=eg,f^c=fg,i^c=i^2102 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 65001);