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 ⋊ #1528 |
| Sylow | C5 ⋊ #68363 |
| Sylow | C3 ⋊ #10604578 |
424 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 80 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,b^2=f,d^2=g,e^2=f,b^a=bd,c^a=cf,d^a=df,i^a=i^2,d^b=dg,e^b=efg,h^c=h^2,i^c=i^4,i^e=i^475 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 9806);