Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
| direct product | SD16×Dic10 |
| Sylow | C5 ⋊ Q8×SD16 |
370 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 141 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 320 |
91 conjugacy classes — view the full character table.
| maximal subgroup of | #12088793, #12088802, #12088853, … |
| maximal normal subgroup of | #12088793, #12088802, #12088853, … |
| maximal quotient of | #102×Dic10, #103×Dic10, SD16×#683, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 13444);