D₁₂₀ #6707

order	240
isoclinism	isoclinic class of #6706
automorphism	Aut(G) = D₃×AGL(1,𝔽₅)×AGL(1,ℤ/8) (order 3840) · Inn(G) = D₆₀ · Out(G) = C₂³×C₄
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

D₁₂₀

44 conjugacy classes of subgroups.

minimal degree	μ(G) = 16
transitive degree	μ_t(G) = 120

A minimal faithful permutation representation — 2 generators on 16 points:

(1,2,3,4,5,6,7,8)(9,10,11)(12,13,14,15,16);(2,8)(3,7)(4,6)(10,11)(13,16)(14,15)

Polycyclic presentation:

2^4,3,5|b^2=cd,c^2=d,b^a=bc,c^a=cd,e^a=e^2,f^a=f^4

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(240, 68);