Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Hall | C3×C5 ⋊ #1875 |
| Sylow | C5 ⋊ #71678 |
| Sylow | C3 ⋊ #10599674 |
824 conjugacy classes of subgroups.
| transitive degree | μt(G) = 960 |
Polycyclic presentation:
2^7,3,5|a^2=f,b^2=dfg,c^2=g,d^2=g,f^2=g,b^a=bd,c^a=ce,h^a=h^2,i^a=i^4,d^b=dg,f^b=fg,h^b=h^2,i^c=i^4162 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 26457);