Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| isoclinism | isoclinic class of #686 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | C2×#64704 |
| Sylow | C5 ⋊ C2×Q8⋊C8 |
280 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 125 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 | #11989896, C4×#64704, #11989906, … |
| maximal normal subgroup of | #11989896, C4×#64704, #11989906, … |
| maximal quotient of | C2×#10597968, C2×#10597971, #11987248, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 3303);