Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| unambiguous semidirect product | GL(2,ℤ/4)⋊AGL(1,𝔽5) |
| Fitting | C24×C5 ⋊ C4×D3 |
| Sylow | C5 ⋊ GL(2,ℤ/4)⋊C4 |
914 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 914 conjugacy classes of subgroups — too many to draw. Only its 66 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 60 |
Polycyclic presentation:
2^5,3,5,2^2|a^2=d,c^a=ce,g^a=g^2,c^b=ce,f^b=f^2,h^b=hi,g^d=g^4,h^f=i,i^f=hi64 conjugacy classes — view the full character table.
| maximal subgroup of | #72231215, D4×AGL(1,𝔽5)×S4, #72243541, … |
| maximal normal subgroup of | D4×AGL(1,𝔽5)×S4 |
| maximal quotient of | #72243541, #72243922, #72260402 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 240035);