Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
| direct product | C2×#66079 |
| Fitting | C22×C5×M16 ⋊ C2 |
| Sylow | C5 ⋊ C2×#568 |
1460 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
148 conjugacy classes — view the full character table.
| maximal subgroup of | #12004626, #12004629, #12004636, … |
| maximal normal subgroup of | #12004626, #12004629, #12004636, … |
| maximal quotient of | C2×#10610245, C2×#10615478, C2×#10610217, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 21137);