Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | D4×#689 |
| Sylow | C5 ⋊ D4×Q16 |
472 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 149 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 320 |
85 conjugacy classes — view the full character table.
| maximal subgroup of | #12088730, #12088733, #12088738, … |
| maximal normal subgroup of | #12088730, #12088733, #12088738, … |
| maximal quotient of | #12089481, #12089487, #12089496, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 17380);