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 ⋊ #3267 |
500 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^7,5|c^2=g,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×#3267, C2×#10615685, #12974369, … |
| maximal normal subgroup of | D5×#3267, C2×#10615685, #12974369, … |
| maximal quotient of | #12088686, #12088806, #12088941, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 17767);