Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | C22×#4011 |
| Fitting | C25×C5 ⋊ C4 |
| Sylow | C5 ⋊ C22×#99 |
1112 conjugacy classes of subgroups; only the 218 normal subgroups are shown.
This group has 1112 conjugacy classes of subgroups — too many to draw. Only its 218 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
76 conjugacy classes — view the full character table.
| maximal subgroup of | #13021794, #13021796, #13021818, … |
| maximal normal subgroup of | #13021794, #13021796, #13021818, … |
| maximal quotient of | C22×#64933, C22×#64914, C2×#10604878, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 19645);