Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C24 |
| unambiguous semidirect product | (C2×AGL(1,𝔽5))⋊SL(2,ℤ/4) |
| Sylow | C5 ⋊ A4⋊#95 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C22 | AGL(1,𝔽5)×S4 |
| commutator | C2×C5×A4 | C42 |
| Fitting, socle | C24×C5 | C4×D3 |
| prime radical, cosocle | C22×D5×A4 | C22 |
| hypocenter | C5×A4 | #95 |
| LCS | G ▷ C2×C5×A4 ▷ C5×A4 | |
| UCS | C1 ◁ C22 | |
822 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 822 conjugacy classes of subgroups — too many to draw. Only its 80 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 120 |
Polycyclic presentation:
2^5,3,5,2^2|a^2=c,b^2=d,b^a=be,g^a=g^2,f^b=f^2,h^b=hi,g^c=g^4,h^f=i,i^f=hi76 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 238129);