Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C24 |
| direct product | C2×#64913 |
| Sylow | C5 ⋊ C2×#324 |
328 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 328 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) = 320 |
76 conjugacy classes — view the full character table.
| maximal subgroup of | #13013632, #13013633, C4×#64913, … |
| maximal normal subgroup of | #13013632, #13013633, C4×#64913, … |
| maximal quotient of | C2×#10598713, #13014633, #13014663, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 6957);