Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| isoclinism | isoclinic class of AΓL(1,𝔽16) |
| automorphism | ? |
| homology | Abelianization (H1) = C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived | AGL(1,𝔽16) ⋊ C8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | AΓL(1,𝔽16) |
| commutator, hypocenter | AGL(1,𝔽16) | C8 |
| Fitting, socle | C25 | ΓL(1,𝔽16) |
| prime radical | C2×AGL(1,𝔽16) | C4 |
| cosocle | #66245⋊C3 | C2 |
| LCS | G ▷ AGL(1,𝔽16) | |
| UCS | C1 ◁ C2 | |
69 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 120 |
Polycyclic presentation:
2^3,3,5,2^4|a^2=b,b^2=c,d^a=d^2,e^a=e^2,f^a=fh,g^a=hi,h^a=g,e^b=e^4,f^b=fgh,g^b=gi,h^b=hi,f^d=g,g^d=fg,h^d=fgi,i^d=ghi,f^e=fgh,g^e=gi,h^e=f,i^e=fghi26 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 239967);