Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4 |
| unambiguous semidirect product | D5⋊#5240 |
| Fitting | C2×C3×C5×#41 ⋊ C4 |
| Hall | C3×C5 ⋊ C2×#410 |
| Sylow | C5 ⋊ C2×#5240 |
| Sylow | C3 ⋊ D5⋊#410 |
1576 conjugacy classes of subgroups.
| transitive degree | μt(G) = 240 |
Polycyclic presentation:
2^7,3,5|a^2=f,c^2=g,b^a=be,e^a=eg,h^a=h^2,i^a=i^2,f^b=fg,i^d=i^4,i^f=i^4144 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 137629);