Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C3×C42×C5 ⋊ C2×C4 |
| Hall | C3×C5 ⋊ #1759 |
| Sylow | C5 ⋊ #69430 |
| Sylow | C3 ⋊ #10604002 |
640 conjugacy classes of subgroups.
| transitive degree | μt(G) = 240 |
Polycyclic presentation:
2^7,3,5|a^2=e,b^2=f,c^2=e,d^2=g,b^a=bd,d^a=dg,f^a=fg,h^a=h^2,i^a=i^3,c^b=cg,i^c=i^2,i^e=i^4114 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 21379);