Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | C2×#64854 |
| Fitting | C2×C42×C5 ⋊ C4 |
| Sylow | C5 ⋊ C2×#354 |
284 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 58 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
58 conjugacy classes — view the full character table.
| maximal subgroup of | #13014493, #13014494, #13014513, … |
| maximal normal subgroup of | #13014493, #13014494, #13014513, … |
| maximal quotient of | C2×#10598687, C2×#10598688, #13023285, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 6223);