Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| isoclinism | isoclinic class of A4⋊AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C24 |
| direct product | C22×A4⋊#170 |
| derived | C5×A4 ⋊ C22×C8 |
| Sylow | C5 ⋊ C22×A4⋊C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | A4⋊AGL(1,𝔽5) |
| commutator, hypocenter | C5×A4 | C22×C8 |
| Frattini | C2 | C22×A4⋊AGL(1,𝔽5) |
| Fitting, socle | C25×C5 | Dic3 |
| prime radical | C23×C5×A4 | C4 |
| cosocle | A4×Dic5 | C23 |
| LCS | G ▷ C5×A4 | |
| UCS | C1 ◁ C23 | |
806 conjugacy classes of subgroups; only the 140 normal subgroups are shown.
This group has 806 conjugacy classes of subgroups — too many to draw. Only its 140 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 480 |
112 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 240085);