Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
| direct product | C2×D5⋊#131 |
| unambiguous semidirect product | D5⋊(C2×#131) |
| Sylow | C5 ⋊ C22×#131 |
1504 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
100 conjugacy classes — view the full character table.
| maximal subgroup of | #13021787, #13021790, #13021831, … |
| maximal normal subgroup of | #13021787, #13021790, #13021831, … |
| maximal quotient of | C2×#10617105, C2×C4×#4131, C4×D5⋊#131, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 21489);