Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C210 |
| direct product | C22×D4×AGL(1,𝔽5) |
| unambiguous semidirect product | D5⋊(C2×C4×D4) |
| Fitting | C22×C5×D4 ⋊ C4 |
| Sylow | C5 ⋊ C22×C4×D4 |
2528 conjugacy classes of subgroups; only the 850 normal subgroups are shown.
This group has 2528 conjugacy classes of subgroups — too many to draw. Only its 850 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 80 |
100 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 21483);