D₅×C₅⋊AGL(1,𝔽₁₁) #72228517

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

Aliases

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₅²×C₁₁	C₂²×C₅
LCS	G ▷ C₅²×C₁₁
UCS	C₁

144 conjugacy classes of subgroups; only the 26 normal subgroups are shown.

normal subgroups only

This group has 144 conjugacy classes of subgroups — too many to draw. Only its 26 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

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

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

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

maximal subgroup of	D₅²×AGL(1,𝔽₁₁), AGL(1,𝔽₅)×C₅⋊AGL(1,𝔽₁₁), #72276391
maximal normal subgroup of	D₅²×AGL(1,𝔽₁₁), AGL(1,𝔽₅)×C₅⋊AGL(1,𝔽₁₁), #72276391

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

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