Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C23×C4 |
| unambiguous semidirect product | D5⋊#5000 |
| Hall | C3×C5 ⋊ C2×#433 |
| Sylow | C5 ⋊ C2×#5000 |
| Sylow | C3 ⋊ D5⋊#433 |
824 conjugacy classes of subgroups.
| transitive degree | μt(G) = 480 |
Polycyclic presentation:
2^7,3,5|a^2=f,c^2=e,f^2=g,b^a=be,h^a=h^2,i^a=i^2,c^b=cg,i^d=i^4,i^f=i^4156 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 139538);