Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
| direct product | C2×#65903 |
| Sylow | C5 ⋊ C2×#557 |
1048 conjugacy classes of subgroups; only the 573 normal subgroups are shown.
This group has 1048 conjugacy classes of subgroups — too many to draw. Only its 573 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 640 |
130 conjugacy classes — view the full character table.
| maximal subgroup of | #11990957, #12065636, #12115876, … |
| maximal normal subgroup of | #11990957, #12065636, #12115876, … |
| maximal quotient of | C2×Q8×#683, C2×#10614192, C2×#10614191, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 19782);