Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
| direct product | C2×#66146 |
| Sylow | C5 ⋊ C2×#519 |
1488 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
148 conjugacy classes — view the full character table.
| maximal subgroup of | #12004622, #12004625, #12004667, … |
| maximal normal subgroup of | #12004622, #12004625, #12004667, … |
| maximal quotient of | C2×#10613875, C2×#10614181, C4×#66146, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 21227);