Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | D5×#335 |
| Fitting | C5×#335 ⋊ C2 |
| Sylow | C5 ⋊ C2×#335 |
200 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 97 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 320 |
112 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#1331, D5×#1332, #12009042, … |
| maximal normal subgroup of | D5×#1331, D5×#1332, #12009042, … |
| maximal quotient of | D5×#1277, #11990484, Dic5×#335, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 1441);