AGL(1,𝔽₁₁)×AGL(1,𝔽₁₉) #49178503

order	37620
automorphism	?
homology	Abelianization (H₁) = C₂²×C₅×C₉ · Schur multiplier (H₂) = C₂

Aliases

direct product	AGL(1,𝔽₁₁)×AGL(1,𝔽₁₉)
unambiguous semidirect product	D₁₁⋊(C₅×AGL(1,𝔽₁₉))
unambiguous semidirect product	(D₁₁×AGL(1,𝔽₁₉))⋊C₅
unambiguous semidirect product	((C₁₁⋊C₅)⋊AGL(1,𝔽₁₉))⋊C₂
unambiguous semidirect product	(AGL(1,𝔽₁₁)×#4296)⋊C₂
unambiguous semidirect product	(C₁₁⋊C₅×AGL(1,𝔽₁₉))⋊C₂

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₁₁×C₁₉	C₂²×C₅×C₉
prime radical	AGL(1,𝔽₁₁)×D₁₉⋊C₃	C₃
cosocle	C₁₁×C₁₉⋊C₃	C₂²×C₃×C₅
LCS	G ▷ C₁₁×C₁₉
UCS	C₁

120 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 41 normal subgroups are shown.

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

μ_t(G) = 209

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37620, 212);