Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| isoclinism | isoclinic class of D80 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C22×D80 |
| Fitting | C22×C5×C16 ⋊ C2 |
| Sylow | C5 ⋊ C22×D16 |
440 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
172 conjugacy classes — view the full character table.
| maximal subgroup of | #12016356, #12016358, #12016391, … |
| maximal normal subgroup of | #12016356, #12016358, #12016391, … |
| maximal quotient of | C22×#64729, C22×#64724, C2×C4×D80, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 15814);