Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
| direct product | D5×#364 |
| Fitting | C5×#364 ⋊ C2 |
| Sylow | C5 ⋊ C2×#364 |
168 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 77 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 80 |
112 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#1335, #12009085, D5×#1336, … |
| maximal normal subgroup of | D5×#1335, #12009085, D5×#1336, … |
| maximal quotient of | D5×#1367, #12010843, D5×#1370, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 2177);