Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27 |
| direct product | C2×#65445 |
| Fitting | C22×C5×D8 ⋊ C2 |
| Sylow | C5 ⋊ C2×#447 |
1048 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 1048 conjugacy classes of subgroups — too many to draw. Only its 173 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
94 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#65445, #12104872, #12104939, … |
| maximal normal subgroup of | C4×#65445, #12104872, #12104939, … |
| maximal quotient of | C2×#10601761, C2×#10601957, C2×#10601764, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 17644);