Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| isoclinism | isoclinic class of A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C5×C32 · Schur multiplier (H2) = C2 |
| direct product | C5×A4×C32 |
| unambiguous semidirect product | (C22×C32)⋊(C3×C5) |
| unambiguous semidirect product | (C22×C5×C32)⋊C3 |
| Fitting, Hall | C22×C5×C32 ⋊ C3 |
| derived | C22 ⋊ C3×C5×C32 |
| Sylow | C22×C32 ⋊ C3×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C32 | A4 |
| commutator, hypocenter | C22 | C3×C5×C32 |
| Frattini | C16 | C2×C5×A4 |
| Fitting | C22×C5×C32 | C3 |
| socle | C23×C5 | C3×C16 |
| prime radical | C2×C5×A4 | C16 |
| cosocle | C22×C16 | C2×C3×C5 |
| LCS | G ▷ C22 | |
| UCS | C1 ◁ C5×C32 | |
80 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 480 |
640 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 236400);