C₁₁×#217 #10587192

order	528
isoclinism	isoclinic class of Dic₆
automorphism	Aut(G) = C₂×C₅×D₃×#120 (order 1920) · Inn(G) = C₂×D₃ · Out(G) = C₂²×C₅×D₄
homology	Abelianization (H₁) = C₂×C₄×C₁₁ · Schur multiplier (H₂) = C₂²

Aliases

Hall	C₃×C₁₁ ⋊ C₂²⋊C₄
Sylow	C₃ ⋊ C₁₁×C₂²⋊C₄

68 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:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(528, 62);