Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
| direct product | C2×#65901 |
| Sylow | C5 ⋊ C2×#557 |
1048 conjugacy classes of subgroups.
| transitive degree | μt(G) = 640 |
130 conjugacy classes — view the full character table.
| maximal subgroup of | #11990956, #11990959, #11991036, … |
| maximal normal subgroup of | #11990956, #11990959, #11991036, … |
| maximal quotient of | C2×C4⋊C4×Dic10, C2×#10605368, C2×#10605372, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 19781);