Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Hall | C3×C5 ⋊ #1459 |
| Sylow | C5 ⋊ #68119 |
| Sylow | C3 ⋊ #10604201 |
664 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 664 conjugacy classes of subgroups — too many to draw. Only its 112 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=e,c^2=g,e^2=g,b^a=bd,d^a=df,i^a=i^2,e^b=ef,i^b=i^4,h^c=h^2,i^c=i^4,i^e=i^4102 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 6583);