Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
| direct product | D5×#497 |
| Fitting | C5×#497 ⋊ C2 |
| Sylow | C5 ⋊ C2×#497 |
564 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 145 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
64 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#1407, D5×#1659, D5×#1661, … |
| maximal normal subgroup of | D5×#1407, D5×#1659, D5×#1661, … |
| maximal quotient of | D5×#1714, D5×#1716, D5×#1718, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 15681);