Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | D4×#700 |
| Sylow | C5 ⋊ D4×M16 |
544 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
70 conjugacy classes — view the full character table.
| maximal subgroup of | #13019020, #13019022, #13019028, … |
| maximal normal subgroup of | #13019020, #13019022, #13019028, … |
| maximal quotient of | D8×#700, #13032703, SD16×#700, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 19233);