Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| isoclinism | isoclinic class of #64845 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4 |
| direct product | C2×#64863 |
| Fitting | C2×C42×C5 ⋊ C4 |
| Sylow | C5 ⋊ C2×H(3,ℤ/4) |
404 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
76 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#64863, #13021572, #13021579, … |
| maximal normal subgroup of | C4×#64863, #13021572, #13021579, … |
| maximal quotient of | C2×#10598526, C2×#10598695, #13015293, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 6238);