Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| isoclinism | isoclinic class of AGL(1,𝔽5)×S4 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C22 |
| direct product | S4×#674 |
| derived | C5×A4 ⋊ C2×C16 |
| Sylow | C5 ⋊ C16×S4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4 | AGL(1,𝔽5)×S4 |
| commutator, hypocenter | C5×A4 | C2×C16 |
| Fitting | C22×C4×C5 | C4×D3 |
| socle | C23×C5 | D3×C8 |
| prime radical | C2×C5×S4 | C8 |
| cosocle | A4×#168 | C22 |
| LCS | G ▷ C5×A4 | |
| UCS | C1 ◁ C4 | |
204 conjugacy classes of subgroups; only the 38 normal subgroups are shown.
This group has 204 conjugacy classes of subgroups — too many to draw. Only its 38 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 240 |
100 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 238047);