Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| isoclinism | isoclinic class of #3993 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C2×D5⋊#108 |
| unambiguous semidirect product | D5⋊(C2×#108) |
| Sylow | C5 ⋊ C22×#108 |
480 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
88 conjugacy classes — view the full character table.
| maximal subgroup of | #13022087, #13022091, #13022100, … |
| maximal normal subgroup of | #13022087, #13022091, #13022100, … |
| maximal quotient of | C2×D5⋊#334, C2×D5⋊#335, C2×#10604694, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 19484);