Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C7 ⋊ #12009 |
242 conjugacy classes of subgroups.
| transitive degree | μt(G) = 896 |
Polycyclic presentation:
2^8,7|a^2=e,b^2=df,d^2=fh,e^2=g,f^2=h,b^a=bd,d^a=df,f^a=fh,c^b=ch,i^b=i^6232 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 81155);