Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | D5⋊#4563 |
| Hall | C3×C5 ⋊ C2×#361 |
| Sylow | C5 ⋊ C2×#4563 |
| Sylow | C3 ⋊ D5⋊#361 |
512 conjugacy classes of subgroups.
| transitive degree | μt(G) = 240 |
Polycyclic presentation:
2^7,3,5|a^2=e,d^2=f,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=dfg,e^b=eg,f^b=fg,i^c=i^4,i^e=i^4102 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 39879);