Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | C2×D5×#99 |
| Fitting | C2×C5×#99 ⋊ C2 |
| Sylow | C5 ⋊ C22×#99 |
1112 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
88 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#1390, #12014245, D5×#1393, … |
| maximal normal subgroup of | D5×#1390, #12014245, D5×#1393, … |
| maximal quotient of | C2×D5×#323, C2×D5×#324, D5×#1459, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 12500);