Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C5 ⋊ C4⋊C32 |
62 conjugacy classes of subgroups.
| transitive degree | μt(G) = 640 |
Polycyclic presentation:
2^7,5|a^2=d,b^2=c,d^2=e,e^2=f,f^2=g,b^a=bc,h^a=h^2,h^b=h^4,h^d=h^4112 conjugacy classes — view the full character table.
| maximal subgroup of | #13014327, #13014328, #13014329, … |
| maximal normal subgroup of | #13014327, #13014328, #13014329, … |
| maximal quotient of | #13014344, #13014352, #13014368, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 737);