Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
| direct product | D5×#488 |
| Fitting | C5×#488 ⋊ C2 |
| Sylow | C5 ⋊ C2×#488 |
412 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 412 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) = 160 |
88 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#1414, C2×D5×#488, D5×#3131, … |
| maximal normal subgroup of | D5×#1414, C2×D5×#488, D5×#3131, … |
| maximal quotient of | D5×#1835, D5×#1933, D5×#1934, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 15449);