Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| isoclinism | isoclinic class of #700 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C23 |
| direct product | C2×#64888 |
| Sylow | C5 ⋊ C2×C4⋊C16 |
184 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 106 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 640 |
112 conjugacy classes — view the full character table.
| maximal subgroup of | #13013701, #13013705, #13013909, … |
| maximal normal subgroup of | #13013701, #13013705, #13013909, … |
| maximal quotient of | C2×#10598523, C2×#10598525, #13025084, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 6789);