Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C23×C8 |
No aliases for this group.
| Sylow | C7 ⋊ #17334 |
806 conjugacy classes of subgroups.
| transitive degree | μt(G) = 448 |
Polycyclic presentation:
2^8,7|a^2=e,b^2=f,e^2=g,f^2=h,c^a=cg,c^b=ch,d^b=dg,i^b=i^6328 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 135284);