Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C5 ⋊ #2969 |
370 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^7,5|a^2=f,c^2=f,d^2=e,f^2=g,b^a=be,h^a=h^2,c^b=cg,h^b=h^4,d^c=dg,h^c=h^3,h^f=h^464 conjugacy classes — view the full character table.
| maximal subgroup of | D5⋊#2969, C2×#10617352, #13044907, … |
| maximal normal subgroup of | D5⋊#2969, C2×#10617352, #13044907, … |
| maximal quotient of | #13033687, #13033689, #13033712, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 19434);