Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4 |
| direct product | C4×#4131 |
| Sylow | C5 ⋊ C4×#131 |
572 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
100 conjugacy classes — view the full character table.
| maximal subgroup of | #13016879, #13016883, #13016887, … |
| maximal normal subgroup of | #13016879, #13016883, #13016887, … |
| maximal quotient of | C8×#4131, #13029002, #13029068, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 19217);