D₁₁×#1044 #72228528

order	2200
automorphism	?
homology	Abelianization (H₁) = C₂×C₄ · Schur multiplier (H₂) = C₂×C₅

Aliases

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₅²×C₁₁	C₂×C₄
prime radical	D₁₁×C₅⋊D₅	C₂
cosocle	C₁₁×C₅⋊D₅	C₂²
LCS	G ▷ C₅²×C₁₁
UCS	C₁

84 conjugacy classes of subgroups.

minimal degree	μ(G) = 21
transitive degree	μ_t(G) = 110

A minimal faithful permutation representation — 2 generators on 21 points:

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

maximal subgroup of	#1044×AGL(1,𝔽₁₁), D₁₁×D₅⋊AGL(1,𝔽₅)
maximal normal subgroup of	#1044×AGL(1,𝔽₁₁), D₁₁×D₅⋊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)(8,9)(10,11)(12,13,16,14,15)(17,18,19,21,20), (1,2,4,6,8,10,11,9,7,5,3)(13,14,15,16)(18,19,20,21));