C₅₃×C₃⋊AGL(1,𝔽₁₁) #31775828

order	17490
isoclinism	isoclinic class of C₃⋊AGL(1,𝔽₁₁)
automorphism	?
homology	Abelianization (H₁) = C₂×C₅×C₅₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₅₃×C₃⋊AGL(1,𝔽₁₁)
unambiguous semidirect product	C₃⋊(C₅₃×AGL(1,𝔽₁₁))
unambiguous semidirect product	(C₁₁⋊C₅)⋊(D₃×C₅₃)
unambiguous semidirect product	D₃₃⋊(C₅×C₅₃)
unambiguous semidirect product	(C₅₃×D₃₃)⋊C₅

	subgroup	G/H
center, hypercenter	C₅₃	C₃⋊AGL(1,𝔽₁₁)
commutator, cosocle, hypocenter	C₃×C₁₁	C₂×C₅×C₅₃
Frattini	C₁	G
Fitting, socle	C₃×C₁₁×C₅₃	C₂×C₅
LCS	G ▷ C₃×C₁₁
UCS	C₁ ◁ C₅₃

32 conjugacy classes of subgroups.

μ_t(G) = 1749

954 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17490, 23);