Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| isoclinism | isoclinic class of AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C32 · Schur multiplier (H2) = C4 |
No aliases for this group.
| derived, Sylow | C5 ⋊ C4×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C16 | AGL(1,𝔽5) |
| commutator, hypocenter | C5 | C4×C32 |
| Frattini | C2×C8 | C2×AGL(1,𝔽5) |
| Fitting | C2×C5×C16 | C4 |
| socle, prime radical | C22×C5 | C2×C16 |
| cosocle | C2×#672 | C22 |
| LCS | G ▷ C5 | |
| UCS | C1 ◁ C2×C16 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 640 |
Polycyclic presentation:
2^7,5|a^2=c,b^2=d,c^2=e,e^2=f,f^2=g,h^a=h^2,h^b=h^4,h^c=h^4160 conjugacy classes — view the full character table.
| maximal subgroup of | C32×#170, #13014064, #170⋊C32, … |
| maximal normal subgroup of | C32×#170, #13014064, #170⋊C32, … |
| maximal quotient of | #13014063, #13014073, #13014368, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 734);