Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×#11756705 |
| unambiguous semidirect product | D5⋊#5394 |
| derived | C5×SL(2,𝔽3) ⋊ C22×C4 |
| Sylow | C5 ⋊ C2×#5394 |
654 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 654 conjugacy classes of subgroups — too many to draw. Only its 66 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
68 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 240000);