Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
| direct product | D5×#483 |
| Fitting | C5×#483 ⋊ C2 |
| Sylow | C5 ⋊ C2×#483 |
460 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 135 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
76 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#1608, D5×#1609, D5×#1611, … |
| maximal normal subgroup of | D5×#1608, D5×#1609, D5×#1611, … |
| maximal quotient of | D5×#1823, D5×#1853, D5×#1872, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 15238);