Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | Dic5×#135 |
| Sylow | C5 ⋊ C4×#135 |
500 conjugacy classes of subgroups; only the 225 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 225 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 | Dic5×#359, #12014531, Dic5×#360, … |
| maximal normal subgroup of | Dic5×#359, #12014531, Dic5×#360, … |
| maximal quotient of | #135×#168, #12068832, #12069050, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 17709);