Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
| direct product | C2×#66153 |
| Sylow | C5 ⋊ C2×#568 |
1460 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
148 conjugacy classes — view the full character table.
| maximal subgroup of | #12004627, #12004630, #12004637, … |
| maximal normal subgroup of | #12004627, #12004630, #12004637, … |
| maximal quotient of | C2×#10613933, C2×#10614242, C4×#66153, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 21236);