Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Sylow | C5 ⋊ #1762 |
388 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 141 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^7,5|a^2=e,b^2=f,c^2=e,d^2=g,f^2=g,b^a=bd,d^a=dg,f^a=fg,c^b=cg,h^b=h^4124 conjugacy classes — view the full character table.
| maximal subgroup of | #11991182, #11991184, #11991196, … |
| maximal normal subgroup of | #11991182, #11991184, #11991196, … |
| maximal quotient of | #11989902, #11989912, #11989947, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 4484);