Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| isoclinism | isoclinic class of #700 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25 |
| direct product | C22×#3998 |
| Sylow | C5 ⋊ C22×M32 |
400 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
112 conjugacy classes — view the full character table.
| maximal subgroup of | #13025425, #13025427, #13025429, … |
| maximal normal subgroup of | #13025425, #13025427, #13025429, … |
| maximal quotient of | C22×#64859, C2×C4×#3998, C22×C22⋊#674, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 19537);