Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | C2×D5⋊#99 |
| unambiguous semidirect product | D5⋊(C2×#99) |
| Fitting | C22×C5×D4 ⋊ C4 |
| Sylow | C5 ⋊ C22×#99 |
1112 conjugacy classes of subgroups; only the 210 normal subgroups are shown.
This group has 1112 conjugacy classes of subgroups — too many to draw. Only its 210 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 80 |
64 conjugacy classes — view the full character table.
| maximal subgroup of | #13021741, #13021742, #13021771, … |
| maximal normal subgroup of | #13021741, #13021742, #13021771, … |
| maximal quotient of | C2×D5⋊#323, C2×D5⋊#324, D5⋊#1459, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 19567);