Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C5×AGL(1,ℤ/8) ⋊ C2 |
| Sylow | C5 ⋊ #3264 |
568 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^7,5|e^2=g,b^a=be,c^a=cf,e^a=eg,d^b=de,e^b=eg,h^c=h^4,e^d=eg73 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#3264, C2×#10615683, #12974372, … |
| maximal normal subgroup of | D5×#3264, C2×#10615683, #12974372, … |
| maximal quotient of | #12088641, #12088761, #12088881, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 17765);