Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25 |
| direct product | C2×#65429 |
| Sylow | C5 ⋊ C2×#504 |
368 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
160 conjugacy classes — view the full character table.
| maximal subgroup of | #12014398, #12014399, #12014404, … |
| maximal normal subgroup of | #12014398, #12014399, #12014404, … |
| maximal quotient of | C2×#10600674, C4×#65429, C2×#10602797, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 17592);