Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| unambiguous semidirect product | D5⋊#5005 |
| Hall | C3×C5 ⋊ C2×#421 |
| Sylow | C5 ⋊ C2×#5005 |
| Sylow | C3 ⋊ D5⋊#421 |
1544 conjugacy classes of subgroups.
| transitive degree | μt(G) = 240 |
Polycyclic presentation:
2^7,3,5|a^2=f,e^2=g,f^2=g,b^a=be,c^a=cg,e^a=eg,h^a=h^2,i^a=i^2,e^b=eg,h^b=h^2,i^d=i^4,i^f=i^4120 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 138599);