Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| isoclinism | isoclinic class of #700 |
| automorphism | ? |
| homology | Abelianization (H1) = C43 · Schur multiplier (H2) = C2×C42 |
| direct product | C4×#4002 |
| Sylow | C5 ⋊ C4×#97 |
360 conjugacy classes of subgroups; only the 190 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 190 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 640 |
112 conjugacy classes — view the full character table.
| maximal subgroup of | #13013215, #13013244, #13013246, … |
| maximal normal subgroup of | #13013215, #13013244, #13013246, … |
| maximal quotient of | C4×#170⋊C8, C8×#4002, #13015251, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 6252);