Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C5 ⋊ #85526 |
600 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 600 conjugacy classes of subgroups — too many to draw. Only its 49 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 240 |
Polycyclic presentation:
2^4,3,5,2^3|c^2=i,d^2=i,g^2=i,h^2=i,b^a=bi,f^a=f^4,c^b=cd,d^b=di,e^b=e^2,g^b=gh,h^b=hi,d^c=di,g^e=h,h^e=ghi,h^g=hi65 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 239274);