Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C26 |
| direct product | C2×D4×#168 |
| Sylow | C5 ⋊ C2×C8×D4 |
616 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
160 conjugacy classes — view the full character table.
| maximal subgroup of | #99×#168, #11989844, #11989848, … |
| maximal normal subgroup of | #99×#168, #11989844, #11989848, … |
| maximal quotient of | C2×D8×#168, C2×SD16×#168, C2×Q16×#168, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 16110);