C₅×D₅×AGL(1,𝔽₁₁) #72228516

order	5500
automorphism	?
homology	Abelianization (H₁) = C₂²×C₅² · Schur multiplier (H₂) = C₂×C₅

Aliases

	subgroup	G/H
center, hypercenter	C₅	D₅×AGL(1,𝔽₁₁)
commutator, cosocle, hypocenter	C₅×C₁₁	C₂²×C₅²
Frattini	C₁	G
Fitting, socle	C₅²×C₁₁	C₂²×C₅
LCS	G ▷ C₅×C₁₁
UCS	C₁ ◁ C₅

256 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:

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

maximal subgroup of	D₅²×AGL(1,𝔽₁₁), C₅×AGL(1,𝔽₅)×AGL(1,𝔽₁₁), #1042×AGL(1,𝔽₁₁)
maximal normal subgroup of	D₅²×AGL(1,𝔽₁₁), C₅×AGL(1,𝔽₅)×AGL(1,𝔽₁₁), #1042×AGL(1,𝔽₁₁)

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

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