Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C7×#1378 ⋊ C2 |
| Sylow | C7 ⋊ #12979 |
456 conjugacy classes of subgroups.
| transitive degree | μt(G) = 448 |
Polycyclic presentation:
2^8,7|a^2=f,b^2=df,e^2=h,f^2=g,g^2=h,b^a=bd,c^a=ce,i^a=i^6,e^b=eh,d^c=dh,e^c=eh,f^c=fh,i^c=i^6196 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 86439);