Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | C2×#65500 |
| Sylow | C5 ⋊ C2×#381 |
1144 conjugacy classes of subgroups; only the 389 normal subgroups are shown.
This group has 1144 conjugacy classes of subgroups — too many to draw. Only its 389 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 320 |
184 conjugacy classes — view the full character table.
| maximal subgroup of | #11988911, #11988913, C2×#10598107, … |
| maximal normal subgroup of | #11988911, #11988913, C2×#10598107, … |
| maximal quotient of | C2×#10602920, C2×#10602327, C4×#65500, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 17839);