Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| unambiguous semidirect product | GL(2,ℤ/4)⋊Dic5 |
| Sylow | C5 ⋊ GL(2,ℤ/4)⋊C4 |
914 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 914 conjugacy classes of subgroups — too many to draw. Only its 89 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:
2^5,3,5,2^2|a^2=e,c^a=cd,g^a=g^4,c^b=cd,f^b=f^2,h^b=hi,h^f=i,i^f=hi106 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 239350);