Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×D5⋊#104 |
| unambiguous semidirect product | D5⋊(C2×#104) |
| Fitting | C2×C5×#41 ⋊ C4 |
| Sylow | C5 ⋊ C22×#104 |
856 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
76 conjugacy classes — view the full character table.
| maximal subgroup of | #13021849, #13021850, #13021852, … |
| maximal normal subgroup of | #13021849, #13021850, #13021852, … |
| maximal quotient of | C2×D5⋊(D4⋊C8), C2×D5⋊(Q8⋊C8), C2×#10605000, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 19616);