Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Hall | C3×C5 ⋊ #1833 |
| Sylow | C5 ⋊ #70657 |
| Sylow | C3 ⋊ #10603852 |
344 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 102 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=e,c^2=d,e^2=g,b^a=bd,c^a=ce,d^a=dg,i^a=i^2,f^b=fg,h^b=h^2,f^c=fg,h^c=h^2,i^f=i^4108 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 24505);