Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×AGL(1,𝔽5)×#226 |
| unambiguous semidirect product | D5⋊(C4×#226) |
| Sylow | C5 ⋊ C2×C4×#226 |
574 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 574 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) = 160 |
80 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 239997);