Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C5×#548 ⋊ C2 |
| Sylow | C5 ⋊ #3285 |
482 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^7,5|b^2=g,d^2=g,e^2=g,b^a=be,c^a=cf,d^a=dg,e^a=eg,d^b=de,e^b=eg,h^b=h^4,e^d=eg85 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#3285, C2×#10615280, #12974589, … |
| maximal normal subgroup of | D5×#3285, C2×#10615280, #12974589, … |
| maximal quotient of | #12089841, #12089847, #12089856, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 17362);