Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | C2×SL(2,ℤ/4)⋊AGL(1,𝔽5) |
| unambiguous semidirect product | D5⋊(SL(2,ℤ/4)⋊C4) |
| Sylow | C5 ⋊ C2×SL(2,ℤ/4)⋊C4 |
998 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 998 conjugacy classes of subgroups — too many to draw. Only its 94 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 120 |
76 conjugacy classes — view the full character table.
| maximal subgroup of | C2×AGL(1,𝔽5)×GL(2,ℤ/4) |
| maximal normal subgroup of | C2×AGL(1,𝔽5)×GL(2,ℤ/4) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 240031);