Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| isoclinism | isoclinic class of AGL(1,𝔽5)×S4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C24 |
| direct product | S4×D5⋊C8 |
| unambiguous semidirect product | D5⋊(C8×S4) |
| unambiguous semidirect product | (D5×S4)⋊C8 |
| derived | C5×A4 ⋊ C22×C8 |
| Sylow | C5 ⋊ C2×C8×S4 |
670 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 670 conjugacy classes of subgroups — too many to draw. Only its 74 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 120 |
100 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 239973);