Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C22×#4088 |
| Fitting | C23×C5×Q8 ⋊ C2 |
| Sylow | C5 ⋊ C22×#137 |
1464 conjugacy classes of subgroups; only the 565 normal subgroups are shown.
This group has 1464 conjugacy classes of subgroups — too many to draw. Only its 565 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 320 |
124 conjugacy classes — view the full character table.
| maximal subgroup of | #12006034, #12006038, #12006047, … |
| maximal normal subgroup of | #12006034, #12006038, #12006047, … |
| maximal quotient of | C22×#65514, C22×#65255, C22×#65253, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 21224);