Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
| direct product | SD16×#168 |
| Sylow | C5 ⋊ C8×SD16 |
180 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 89 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 320 |
112 conjugacy classes — view the full character table.
| maximal subgroup of | C8×D5×SD16, C2×SD16×#168, C8×#4062, … |
| maximal normal subgroup of | C8×D5×SD16, C2×SD16×#168, C8×#4062, … |
| maximal quotient of | #102×#168, #103×#168, #106×#168, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 3768);