Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4 |
| direct product | C2×#65519 |
| Sylow | C5 ⋊ C2×#391 |
928 conjugacy classes of subgroups; only the 405 normal subgroups are shown.
This group has 928 conjugacy classes of subgroups — too many to draw. Only its 405 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 640 |
136 conjugacy classes — view the full character table.
| maximal subgroup of | #12004668, #12004670, #12005569, … |
| maximal normal subgroup of | #12004668, #12004670, #12005569, … |
| maximal quotient of | C2×#10602356, C2×#10602357, C4×#65519, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 17874);