Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#65489 |
| Sylow | C5 ⋊ C2×#471 |
468 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 468 conjugacy classes of subgroups — too many to draw. Only its 141 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
76 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#65489, #12106170, #12106220, … |
| maximal normal subgroup of | C4×#65489, #12106170, #12106220, … |
| maximal quotient of | C2×#10601797, C2×#10601925, C2×#10601800, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 17754);