Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| isoclinism | isoclinic class of #700 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
| direct product | C23×#704 |
| Sylow | C5 ⋊ C23×M16 |
1720 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
112 conjugacy classes — view the full character table.
| maximal subgroup of | #13021643, #13021681, #13021711, … |
| maximal normal subgroup of | #13021643, #13021681, #13021711, … |
| maximal quotient of | C23×#4002, C22×C4×#704, C23×C22⋊#170, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 21500);