Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C5 ⋊ #1398 |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^7,5|a^2=c,b^2=d,c^2=e,e^2=f,f^2=g,b^a=bf,d^a=dg,h^a=h^2,c^b=cg,h^b=h^4,h^c=h^476 conjugacy classes — view the full character table.
| maximal subgroup of | #13014077, #13014078, #13014081, … |
| maximal normal subgroup of | #13014077, #13014078, #13014081, … |
| maximal quotient of | #13014070, #13014074, #13014371, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 738);