Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
| direct product | D5×#491 |
| Fitting | C5×#491 ⋊ C2 |
| Sylow | C5 ⋊ C2×#491 |
384 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 125 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 320 |
64 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#1356, D5×#1413, D5×#1662, … |
| maximal normal subgroup of | D5×#1356, D5×#1413, D5×#1662, … |
| maximal quotient of | D5×#1836, D5×#1935, D5×#1960, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 15549);