Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C26 |
| direct product | C2×D5×C4⋊C8 |
| Fitting | C2×C5×C4⋊C8 ⋊ C2 |
| Sylow | C5 ⋊ C22×C4⋊C8 |
640 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
160 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#1277, #11988760, #11988774, … |
| maximal normal subgroup of | D5×#1277, #11988760, #11988774, … |
| maximal quotient of | C2×D5×#334, C2×D5×#335, D5×#1564, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 12822);