Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Sylow | C5 ⋊ #2879 |
764 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^7,5|a^2=f,f^2=g,b^a=be,d^a=dg,h^a=h^2,c^b=cg,h^d=h^4,h^f=h^464 conjugacy classes — view the full character table.
| maximal subgroup of | #13021736, #13021738, #13021779, … |
| maximal normal subgroup of | #13021736, #13021738, #13021779, … |
| maximal quotient of | #13029435, #13029440, #13029444, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 19623);