Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Hall | C3×C5 ⋊ #1589 |
| Sylow | C5 ⋊ #70859 |
| Sylow | C3 ⋊ #10604795 |
360 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 90 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 960 |
Polycyclic presentation:
2^7,3,5|a^2=e,c^2=e,d^2=f,e^2=g,b^a=bd,c^a=cg,d^a=df,h^a=h^2,i^a=i^3,c^b=cg,d^b=df,i^c=i^2,i^e=i^496 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 12994);