Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| isoclinism | isoclinic class of #3993 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
| direct product | C2×#64861 |
| Sylow | C5 ⋊ C2×#364 |
168 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 82 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 | #13013895, #13013897, #13013899, … |
| maximal normal subgroup of | #13013895, #13013897, #13013899, … |
| maximal quotient of | C2×#10598523, #13025033, C2×#10598525, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 6236);