Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | SD16⋊(C7⋊C16) |
| Sylow | C7 ⋊ SD16⋊C16 |
232 conjugacy classes of subgroups.
| transitive degree | μt(G) = 896 |
Polycyclic presentation:
2^8,7|a^2=e,c^2=e,d^2=f,e^2=g,g^2=h,b^a=bd,c^a=cf,d^a=df,i^a=i^6,d^b=df,i^c=i^6256 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 81380);