Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C24 |
| direct product | C2×#64871 |
| Sylow | C5 ⋊ C2×D4⋊C8 |
344 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 106 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 320 |
76 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#64871, #13016837, #13016843, … |
| maximal normal subgroup of | C4×#64871, #13016837, #13016843, … |
| maximal quotient of | C2×#10598712, C2×#10598714, #13014620, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 6350);