Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Hall | C3×C5 ⋊ #1584 |
| Sylow | C5 ⋊ #70903 |
| Sylow | C3 ⋊ #10604064 |
304 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 97 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1920 |
Polycyclic presentation:
2^7,3,5|a^2=e,b^2=f,c^2=ef,d^2=f,e^2=g,b^a=bd,c^a=cg,d^a=df,h^a=h^2,i^a=i^2,d^b=df,i^b=i^4,h^c=h^2,i^c=i^2,i^e=i^4108 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 12500);