Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
| direct product | C2×#65973 |
| Fitting | C2×C5×C22⋊Q8 ⋊ C2 |
| Sylow | C5 ⋊ C2×#552 |
1124 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
106 conjugacy classes — view the full character table.
| maximal subgroup of | #11990900, #12065503, #12115463, … |
| maximal normal subgroup of | #11990900, #12065503, #12115463, … |
| maximal quotient of | C2×#10607034, C2×#10607931, C2×#10605612, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 19967);