Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C2×C7×Q8⋊C8 ⋊ C2 |
| Sylow | C7 ⋊ #9640 |
582 conjugacy classes of subgroups.
| transitive degree | μt(G) = 896 |
Polycyclic presentation:
2^8,7|a^2=f,b^2=df,c^2=e,d^2=g,f^2=h,b^a=bd,c^a=ce,d^a=dg,c^b=cg,i^c=i^6232 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 68351);