Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C7×#2112 ⋊ C2 |
| Sylow | C7 ⋊ #12683 |
936 conjugacy classes of subgroups.
| transitive degree | μt(G) = 448 |
Polycyclic presentation:
2^8,7|a^2=f,d^2=h,f^2=g,g^2=h,b^a=bd,c^a=ce,i^a=i^6,d^b=dh,f^b=fh,i^b=i^6244 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 85014);