Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C5 ⋊ #1328 |
90 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^7,5|a^2=d,b^2=e,d^2=f,f^2=g,b^a=bc,c^a=ce,e^a=eg,c^b=cg,d^b=de,h^b=h^4,d^c=dg70 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#1328, C2×#10598024, #12008492, … |
| maximal normal subgroup of | D5×#1328, C2×#10598024, #12008492, … |
| maximal quotient of | #11985938, #11985940, #11985941, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 106);