Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | C22×#4007 |
| unambiguous semidirect product | D5⋊(C2×#102) |
| Fitting | C22×C5×D4 ⋊ C4 |
| Sylow | C5 ⋊ C22×#102 |
1072 conjugacy classes of subgroups; only the 258 normal subgroups are shown.
This group has 1072 conjugacy classes of subgroups — too many to draw. Only its 258 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 | #13021876, #13021877, #13022283, … |
| maximal normal subgroup of | #13021876, #13021877, #13022283, … |
| maximal quotient of | C22×D4⋊#170, C2×D5⋊(D4⋊C8), C22×#64871, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 19563);