Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | SD16⋊(C3⋊#168) |
| Hall | C3×C5 ⋊ SD16⋊C8 |
| Sylow | C5 ⋊ SD16⋊(C3⋊C8) |
| Sylow | C3 ⋊ SD16⋊#168 |
352 conjugacy classes of subgroups.
| transitive degree | μt(G) = 960 |
Polycyclic presentation:
2^7,3,5|a^2=e,c^2=e,d^2=f,e^2=g,b^a=bd,c^a=cf,d^a=df,h^a=h^2,i^a=i^4,d^b=df,h^c=h^2,i^c=i^4240 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 11988);