C₃×#4324 #10587173

order	528
isoclinism	isoclinic class of #4323
automorphism	Aut(G) = C₂²×D₄×AGL(1,𝔽₁₁) (order 3520) · Inn(G) = C₂²⋊D₁₁ · Out(G) = C₂³×C₅
homology	Abelianization (H₁) = C₂²×C₃ · Schur multiplier (H₂) = C₁

Aliases

Hall	C₃×C₁₁ ⋊ SD₁₆
Sylow	C₁₁ ⋊ C₃×SD₁₆

40 conjugacy classes of subgroups.

minimal degree	μ(G) = 22
transitive degree	μ_t(G) = 264

A minimal faithful permutation representation — 2 generators on 22 points:

(1,2,3)(4,5,7,9,11,13,14,12,10,8,6)(16,19)(17,22)(20,21);(5,6)(7,8)(9,10)(11,12)(13,14)(15,16,18,21)(17,19,22,20)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(528, 43);