Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C22×#4057 |
| Fitting | C22×C5×D8 ⋊ C2 |
| Sylow | C5 ⋊ C22×AGL(1,ℤ/8) |
1720 conjugacy classes of subgroups; only the 525 normal subgroups are shown.
This group has 1720 conjugacy classes of subgroups — too many to draw. Only its 525 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
100 conjugacy classes — view the full character table.
| maximal subgroup of | #12100658, #12100682, #12100694, … |
| maximal normal subgroup of | #12100658, #12100682, #12100694, … |
| maximal quotient of | C22×#65059, C22×#65060, C22×#65170, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 21154);