Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24 |
| direct product | D5×#338 |
| Fitting | C5×#338 ⋊ C2 |
| Sylow | C5 ⋊ C2×#338 |
372 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 135 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 80 |
88 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#1341, D5×#1342, #12009460, … |
| maximal normal subgroup of | D5×#1341, D5×#1342, #12009460, … |
| maximal quotient of | D5×#1275, #11988717, #11988720, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 1595);