Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | AGL(1,𝔽5)×A4⋊Q8 |
| unambiguous semidirect product | (A4×AGL(1,𝔽5))⋊Q8 |
| Sylow | C5 ⋊ C4×A4⋊Q8 |
650 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 650 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 120 |
70 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 239981);