Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| isoclinism | isoclinic class of Dic10 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25 |
| direct product | C22×#3930 |
| Fitting | C22×C5×C16 ⋊ C2 |
| Sylow | C5 ⋊ C22×M32 |
400 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
208 conjugacy classes — view the full character table.
| maximal subgroup of | #12014138, #12014141, #12014171, … |
| maximal normal subgroup of | #12014138, #12014141, #12014171, … |
| maximal quotient of | C22×#64722, C2×C4×#3930, C22×#64727, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 15812);