Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of A4×AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C8×C9 · Schur multiplier (H2) = C2 |
| direct product | C22⋊C9×#170 |
| unambiguous semidirect product | (C22×#170)⋊C9 |
| derived | C22×C5 ⋊ C8×C9 |
| Hall | C22×#170 ⋊ C9 |
| Sylow | C5 ⋊ C8×C22⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2×C3 | A4×AGL(1,𝔽5) |
| commutator, hypocenter | C22×C5 | C8×C9 |
| Fitting, socle, prime radical | C23×C3×C5 | C3×C4 |
| cosocle | C22×C3×Dic5 | C2×C3 |
| LCS | G ▷ C22×C5 | |
| UCS | C1 ◁ C2×C3 | |
88 conjugacy classes of subgroups.
| minimal degree | μ(G) = 26 |
| transitive degree | μt(G) = 360 |
120 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 1462);