Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
| direct product | C4×#4009 |
| Fitting | C4×C5×Q8 ⋊ C4 |
| Sylow | C5 ⋊ C4×#103 |
332 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 110 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 | C8×#4009, #13016961, #13016966, … |
| maximal normal subgroup of | C8×#4009, #13016961, #13016966, … |
| maximal quotient of | C4×Q8⋊#170, C4×#64872, #13016851, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 6535);