C₁₁⋊(ΓL(1,𝔽₈)⋊#1039) #37528360

order	23100
automorphism	?
homology	Abelianization (H₁) = C₃×C₄ · Schur multiplier (H₂) = C₅

Aliases

unambiguous semidirect product	C₁₁⋊(ΓL(1,𝔽₈)⋊#1039)
unambiguous semidirect product	ΓL(1,𝔽₈)⋊(C₁₁⋊#1039)

	subgroup	G/H
center, Frattini, hypercenter	C₂	C₅⋊(C₅⋊(C₁₁⋊AGL(1,𝔽₇)))
commutator, hypocenter	C₅²×C₇×C₁₁	C₃×C₄
Fitting, socle, cosocle	C₂×C₅²×C₇×C₁₁	C₂×C₃
prime radical	C₂×C₅²×C₁₁×ΓL(1,𝔽₈)	C₂
LCS	G ▷ C₅²×C₇×C₁₁
UCS	C₁ ◁ C₂

192 conjugacy classes of subgroups.

μ_t(G) = 7700

Polycyclic presentation:

2,3,5^2,7,11,2|a^2=g,c^a=c^4,d^a=d^4,e^a=e^6,f^a=f^10,e^b=e^2

1384 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 171);