Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C5×#407 ⋊ C2 |
| Sylow | C5 ⋊ #1462 |
440 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 81 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 80 |
Polycyclic presentation:
2^7,5|a^2=e,e^2=g,b^a=bd,c^a=cg,d^a=df,e^b=ef,h^b=h^488 conjugacy classes — view the full character table.
| maximal subgroup of | #11990809, #11990812, #11991918, … |
| maximal normal subgroup of | #11990809, #11990812, #11991918, … |
| maximal quotient of | #11987430, #11987432, #11987443, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 2842);