Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| isoclinism | isoclinic class of #64686 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22 |
| direct product | C2×#64686 |
| Sylow | C5 ⋊ C2×#347 |
168 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 109 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
124 conjugacy classes — view the full character table.
| maximal subgroup of | #11986467, #11986468, #11986469, … |
| maximal normal subgroup of | #11986467, #11986468, #11986469, … |
| maximal quotient of | C2×#10597933, #12008301, #12008342, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 2677);