Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×#64905 |
| Sylow | C5 ⋊ C2×#359 |
224 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 66 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 320 |
58 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#64905, #13025883, #13025887, … |
| maximal normal subgroup of | C4×#64905, #13025883, #13025887, … |
| maximal quotient of | C2×#10598801, C2×#10598610, #13023686, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 6869);