Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Hall | C3×C5 ⋊ #1886 |
| Sylow | C5 ⋊ #71660 |
| Sylow | C3 ⋊ #10602453 |
648 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 648 conjugacy classes of subgroups — too many to draw. Only its 167 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 480 |
Polycyclic presentation:
2^7,3,5|a^2=f,b^2=df,c^2=g,d^2=g,f^2=g,b^a=bd,c^a=ce,e^a=eg,h^a=h^2,i^a=i^4,d^b=dg,e^b=eg,f^b=fg,d^c=dg,f^c=fg270 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 27183);