Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| isoclinism | isoclinic class of A4⋊AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | A4⋊#3928 |
| derived | C5×A4 ⋊ C32 |
| Sylow | C5 ⋊ A4⋊C32 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C8 | A4⋊AGL(1,𝔽5) |
| commutator, hypocenter | C5×A4 | C32 |
| Fitting | C22×C5×C8 | Dic3 |
| socle | C23×C5 | C3⋊C16 |
| prime radical | C2×C5×A4 | C16 |
| cosocle | A4×#672 | C2 |
| LCS | G ▷ C5×A4 | |
| UCS | C1 ◁ C8 | |
80 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 480 |
Polycyclic presentation:
2^5,3,5,2^2|a^2=b,b^2=c,c^2=d,d^2=e,f^a=f^2,g^a=g^2,h^a=hi,g^b=g^4,h^f=i,i^f=hi112 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 237284);