C₄²×D₁₁ #66924

order	352
isoclinism	isoclinic class of D₁₁
automorphism	?
homology	Abelianization (H₁) = C₂×C₄² · Schur multiplier (H₂) = C₂²×C₄

Aliases

C₄²×D₁₁

Fitting	C₄²×C₁₁ ⋊ C₂
derived, Sylow	C₁₁ ⋊ C₂×C₄²

108 conjugacy classes of subgroups.

minimal degree	μ(G) = 19
transitive degree	μ_t(G) = 176

A minimal faithful permutation representation — 3 generators on 19 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(352, 66);