Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C2×#65735 |
| unambiguous semidirect product | D5⋊#440 |
| Fitting | C2×C5×SD16 ⋊ C4 |
| Sylow | C5 ⋊ C2×#440 |
544 conjugacy classes of subgroups; only the 170 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 170 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 80 |
58 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#65735, AGL(1,𝔽5)×#440, #13033795, … |
| maximal normal subgroup of | C4×#65735, AGL(1,𝔽5)×#440, #13033795, … |
| maximal quotient of | C2×SD16⋊#170, C2×#10603969, C2×#10603937, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 19509);