Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×#65755 |
| Sylow | C5 ⋊ C2×#407 |
1008 conjugacy classes of subgroups; only the 234 normal subgroups are shown.
This group has 1008 conjugacy classes of subgroups — too many to draw. Only its 234 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
88 conjugacy classes — view the full character table.
| maximal subgroup of | #13015601, #13015625, C2×#10598692, … |
| maximal normal subgroup of | #13015601, #13015625, C2×#10598692, … |
| maximal quotient of | C2×#10604880, C2×#10604882, C2×#10604162, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 19545);