Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | D5⋊#5423 |
| Sylow | C5 ⋊ C2×#5423 |
626 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 626 conjugacy classes of subgroups — too many to draw. Only its 78 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^4,3,5,2^3|a^2=d,b^2=i,d^2=i,g^2=i,h^2=i,c^a=ci,e^a=e^2,f^a=f^2,g^a=gh,h^a=hi,f^d=f^4,g^e=h,h^e=ghi,h^g=hi80 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 240077);