Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| isoclinism | isoclinic class of #64671 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | C2×#64685 |
| Sylow | C5 ⋊ C2×#330 |
232 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 85 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 640 |
118 conjugacy classes — view the full character table.
| maximal subgroup of | #11990217, C4×#64685, #11990225, … |
| maximal normal subgroup of | #11990217, C4×#64685, #11990225, … |
| maximal quotient of | C2×#10597968, C2×#10597969, #11987271, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 2675);