Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C2×#65475 |
| Fitting | C22×C5×Q16 ⋊ C2 |
| Sylow | C5 ⋊ C2×#451 |
740 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 740 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) = 320 |
94 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#65475, #12104905, #12104972, … |
| maximal normal subgroup of | C4×#65475, #12104905, #12104972, … |
| maximal quotient of | C2×#10601773, C2×#10601969, C2×#10601776, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 17695);