Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C5 ⋊ #2906 |
484 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^7,5|a^2=f,b^2=e,f^2=g,b^a=be,h^a=h^2,h^b=h^4,d^c=dg,h^f=h^470 conjugacy classes — view the full character table.
| maximal subgroup of | #13019756, #13019760, #13019764, … |
| maximal normal subgroup of | #13019756, #13019760, #13019764, … |
| maximal quotient of | #13031466, #13031471, #13031472, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 19220);