Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×#65798 |
| Sylow | C5 ⋊ C2×#407 |
1008 conjugacy classes of subgroups; only the 250 normal subgroups are shown.
This group has 1008 conjugacy classes of subgroups — too many to draw. Only its 250 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
88 conjugacy classes — view the full character table.
| maximal subgroup of | #13015534, #13015541, #13015546, … |
| maximal normal subgroup of | #13015534, #13015541, #13015546, … |
| maximal quotient of | C2×#10605022, C2×#10604881, C2×#10604883, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 19647);