Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| isoclinism | isoclinic class of A4×AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C32 · Schur multiplier (H2) = C2 |
| direct product | A4×#3928 |
| unambiguous semidirect product | (C22×#3928)⋊C3 |
| derived | C22×C5 ⋊ C3×C32 |
| Hall | C22×#3928 ⋊ C3 |
| Sylow | C5 ⋊ A4×C32 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C8 | A4×AGL(1,𝔽5) |
| commutator, hypocenter | C22×C5 | C3×C32 |
| Fitting | C22×C5×C8 | C3×C4 |
| socle | C23×C5 | C3×C16 |
| prime radical | C2×C5×A4 | C16 |
| cosocle | C22×#672 | C2×C3 |
| LCS | G ▷ C22×C5 | |
| UCS | C1 ◁ C8 | |
80 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 480 |
160 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 237299);