Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| isoclinism | isoclinic class of Dic10 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
| direct product | C22×#4047 |
| Fitting | C23×C5×C8 ⋊ C2 |
| Sylow | C5 ⋊ C22×#131 |
1504 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
208 conjugacy classes — view the full character table.
| maximal subgroup of | #12004711, #12004715, #12004733, … |
| maximal normal subgroup of | #12004711, #12004715, #12004733, … |
| maximal quotient of | C22×#64978, C22×#65390, C2×C4×#4047, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 21130);