Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
| direct product | C22×#4133 |
| Sylow | C5 ⋊ C22×#131 |
1504 conjugacy classes of subgroups; only the 770 normal subgroups are shown.
This group has 1504 conjugacy classes of subgroups — too many to draw. Only its 770 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 320 |
100 conjugacy classes — view the full character table.
| maximal subgroup of | #13021808, #13021884, #13033141, … |
| maximal normal subgroup of | #13021808, #13021884, #13033141, … |
| maximal quotient of | C22×#65701, C2×C4×#4133, C22×#65787, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 21485);