Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×#65794 |
| unambiguous semidirect product | D5⋊#416 |
| Fitting | C2×C5×#41 ⋊ C4 |
| Sylow | C5 ⋊ C2×#416 |
792 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
76 conjugacy classes — view the full character table.
| maximal subgroup of | #13021846, #13021847, #13021855, … |
| maximal normal subgroup of | #13021846, #13021847, #13021855, … |
| maximal quotient of | C2×#10605000, D5⋊#1476, C2×#10604401, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 19613);