Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
| direct product | C2×D5×#126 |
| Fitting | C2×C5×#126 ⋊ C2 |
| Sylow | C5 ⋊ C22×#126 |
1320 conjugacy classes of subgroups; only the 517 normal subgroups are shown.
This group has 1320 conjugacy classes of subgroups — too many to draw. Only its 517 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
112 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#1473, #12065393, C4×D5×#126, … |
| maximal normal subgroup of | D5×#1473, #12065393, C4×D5×#126, … |
| maximal quotient of | C2×D5×#383, C2×D5×#387, C2×D5×#388, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 20094);