Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Fitting | C5×#125 ⋊ C4 |
| Sylow | C5 ⋊ #1412 |
94 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
Polycyclic presentation:
2^7,5|a^2=d,b^2=f,c^2=fg,e^2=g,b^a=bc,c^a=ce,e^a=ef,f^a=fg,h^a=h^3,c^b=cf,d^b=def,e^b=eg,d^c=dfg,e^d=eg,h^d=h^428 conjugacy classes — view the full character table.
| maximal subgroup of | #13014549, #13014551, #13014553, … |
| maximal normal subgroup of | #13014549, #13014551, #13014553, … |
| maximal quotient of | #13014134, #13014156, #13014256, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 821);