Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C2×C3×C42×C5 ⋊ C22 |
| Hall | C3×C5 ⋊ D4×#41 |
| Sylow | C5 ⋊ D4×#235 |
| Sylow | C3 ⋊ #10618139 |
3296 conjugacy classes of subgroups.
| transitive degree | μt(G) = 480 |
Polycyclic presentation:
2^7,3,5|e^2=f,b^a=bf,c^a=cg,h^a=h^2,d^b=df,i^c=i^4,h^d=h^2,i^d=i^4210 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 208846);