C₃×C₅×SD₁₆ #6726

order	240
nilpotency class	3
isoclinism	isoclinic class of D₈
automorphism	Aut(G) = C₂²×C₄×D₄ (order 128) · Inn(G) = D₄ · Out(G) = C₂²×C₄
homology	Abelianization (H₁) = C₂²×C₃×C₅ · Schur multiplier (H₂) = C₁

Aliases

C₃×C₅×SD₁₆

	subgroup	G/H
center, socle	C₂×C₃×C₅	D₄
commutator, Frattini, cosocle	C₄	C₂²×C₃×C₅
prime radical	C₃×C₅×D₄	C₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃×C₅ ◁ C₃×C₄×C₅ ◁ G

40 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);(10,12)(11,15)(14,16)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(240, 87);