Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| isoclinism | isoclinic class of A4⋊AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | C23×A4⋊AGL(1,𝔽5) |
| unambiguous semidirect product | D5⋊(C22×SL(2,ℤ/4)) |
| Fitting, socle | C25×C5 ⋊ Dic3 |
| derived | C5×A4 ⋊ C23×C4 |
| Sylow | C5 ⋊ C23×SL(2,ℤ/4) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | A4⋊AGL(1,𝔽5) |
| commutator, hypocenter | C5×A4 | C23×C4 |
| Frattini | C1 | G |
| Fitting, socle | C25×C5 | Dic3 |
| prime radical | C23×D5×A4 | C2 |
| cosocle | D5×A4 | C24 |
| LCS | G ▷ C5×A4 | |
| UCS | C1 ◁ C23 | |
3310 conjugacy classes of subgroups; only the 300 normal subgroups are shown.
This group has 3310 conjugacy classes of subgroups — too many to draw. Only its 300 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 120 |
112 conjugacy classes — view the full character table.
| maximal subgroup of | C2×A4×A4⋊AGL(1,𝔽5), C22×#11756729 |
| maximal normal subgroup of | C2×A4×A4⋊AGL(1,𝔽5), C22×#11756729 |
| maximal quotient of | C22×#11756729 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 240403);