Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | D5⋊#4567 |
| Hall | C3×C5 ⋊ C2×#359 |
| Sylow | C5 ⋊ C2×#4567 |
| Sylow | C3 ⋊ D5⋊#359 |
448 conjugacy classes of subgroups.
| transitive degree | μt(G) = 480 |
Polycyclic presentation:
2^7,3,5|a^2=e,d^2=fg,e^2=g,f^2=g,b^a=bd,d^a=df,f^a=fg,h^a=h^2,i^a=i^2,d^b=df,f^b=fg,i^c=i^4,i^e=i^4114 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 39709);