Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#65208 |
| Fitting | C2×C5×Q32 ⋊ C2 |
| Sylow | C5 ⋊ C2×#508 |
368 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 117 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 320 |
88 conjugacy classes — view the full character table.
| maximal subgroup of | #12019733, #12019738, #12019775, … |
| maximal normal subgroup of | #12019733, #12019738, #12019775, … |
| maximal quotient of | C2×#10600013, C2×#10600118, C2×#10600110, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 15839);