Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C2×D5×#137 |
| Fitting | C2×C5×#137 ⋊ C2 |
| Sylow | C5 ⋊ C22×#137 |
1464 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
88 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#1882, #12100820, D5×#1902, … |
| maximal normal subgroup of | D5×#1882, #12100820, D5×#1902, … |
| maximal quotient of | C2×D5×#419, C2×D5×#417, C2×D5×#428, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 21176);