Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Hall | C3×C5 ⋊ C4×#137 |
| Sylow | C5 ⋊ C4×#909 |
| Sylow | C3 ⋊ #10610931 |
968 conjugacy classes of subgroups.
| transitive degree | μt(G) = 960 |
Polycyclic presentation:
2^7,3,5|a^2=f,b^2=g,c^2=f,e^2=g,b^a=be,d^a=dg,e^a=eg,h^a=h^2,e^b=eg,h^b=h^2,i^b=i^4,i^c=i^4168 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 142627);