A₄×Dic₁₁⋊C₅ #72276515

order	2640
automorphism	?
homology	Abelianization (H₁) = C₃×C₄×C₅ · Schur multiplier (H₂) = C₂

Aliases

	subgroup	G/H
center, Frattini, hypercenter	C₂	A₄×AGL(1,𝔽₁₁)
commutator, hypocenter	C₂²×C₁₁	C₃×C₄×C₅
Fitting, socle, cosocle	C₂³×C₁₁	C₂×C₃×C₅
prime radical	C₂×A₄×C₁₁⋊C₅	C₂
LCS	G ▷ C₂²×C₁₁
UCS	C₁ ◁ C₂

76 conjugacy classes of subgroups.

minimal degree	μ(G) = 19
transitive degree	μ_t(G) = 132

A minimal faithful permutation representation — 2 generators on 19 points:

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

maximal subgroup of	A₄×(C₁₁⋊C₅)⋊AGL(1,𝔽₅)
maximal quotient of	A₄×(C₁₁⋊C₅)⋊AGL(1,𝔽₅)

Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:

gap> G := Group((2,3,4)(5,6,7,8)(10,14,15,17,16,11,12,13,18,19), (1,4)(2,3)(9,10,13,12,16,18,17,19,14,15,11));