Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4 |
| direct product | C2×#65767 |
| unambiguous semidirect product | D5⋊#418 |
| Fitting | C22×C5×D4 ⋊ C4 |
| Sylow | C5 ⋊ C2×#418 |
1008 conjugacy classes of subgroups; only the 210 normal subgroups are shown.
This group has 1008 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 | #13021838, #13021839, #13021866, … |
| maximal normal subgroup of | #13021838, #13021839, #13021866, … |
| maximal quotient of | C2×#10604922, D5⋊#1478, C2×#10604403, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 19564);