Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C5 ⋊ #2905 |
484 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^7,5|a^2=f,b^2=e,f^2=g,b^a=be,d^a=dg,c^b=cg,h^b=h^4124 conjugacy classes — view the full character table.
| maximal subgroup of | #12005342, #12005344, #12005345, … |
| maximal normal subgroup of | #12005342, #12005344, #12005345, … |
| maximal quotient of | #12068444, #12068448, #12068452, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 17563);