Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| isoclinism | isoclinic class of AGL(1,𝔽5)×C22⋊A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C25 |
| direct product | C2×AGL(1,𝔽5)×C22⋊A4 |
| unambiguous semidirect product | D5⋊(C4×C22⋊A4) |
| Fitting, socle | C25×C5 ⋊ C3×C4 |
| derived | C24×C5 ⋊ C2×C3×C4 |
| Hall | C25×AGL(1,𝔽5) ⋊ C3 |
| Sylow | C5 ⋊ C2×C4×C22⋊A4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | AGL(1,𝔽5)×C22⋊A4 |
| commutator, hypocenter | C24×C5 | C2×C3×C4 |
| Frattini | C1 | G |
| Fitting, socle | C25×C5 | C3×C4 |
| prime radical | C2×D5×C22⋊A4 | C2 |
| cosocle | C24×D5 | C22×C3 |
| LCS | G ▷ C24×C5 | |
| UCS | C1 ◁ C2 | |
3704 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 3704 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) = 60 |
80 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 240406);