Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | D4×#687 |
| Sylow | C5 ⋊ D4×SD16 |
546 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 546 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) = 160 |
85 conjugacy classes — view the full character table.
| maximal subgroup of | #12088658, #12088666, #12088673, … |
| maximal normal subgroup of | #12088658, #12088666, #12088673, … |
| maximal quotient of | #12088767, #12088782, #12088797, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 17306);