Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C5×#546 ⋊ C2 |
| Sylow | C5 ⋊ #3275 |
498 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^7,5|a^2=g,b^2=g,e^2=g,b^a=be,c^a=cf,e^a=eg,c^b=cg,d^b=de,e^b=eg,h^b=h^4,e^d=eg79 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#3275, C2×#10615239, #12974476, … |
| maximal normal subgroup of | D5×#3275, C2×#10615239, #12974476, … |
| maximal quotient of | #12090594, #12090685, #12090700, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 17321);