Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| isoclinism | isoclinic class of #686 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
| direct product | C4×#3940 |
| Sylow | C5 ⋊ C4×#106 |
280 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 145 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 640 |
136 conjugacy classes — view the full character table.
| maximal subgroup of | #11990523, C8×#3940, #11990538, … |
| maximal normal subgroup of | #11990523, C8×#3940, #11990538, … |
| maximal quotient of | C4×#64700, #11990490, #11990508, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 2354);