Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C22×C5×C22⋊C4 ⋊ D3 |
| Sylow | C5 ⋊ GL(2,ℤ/4)⋊C4 |
914 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 914 conjugacy classes of subgroups — too many to draw. Only its 87 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|c^2=d,b^a=be,f^a=f^2,g^a=g^4,h^a=hi,c^b=ce,h^f=i,i^f=hi130 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 239397);