C₁₁⋊(#1039⋊ΓL(1,𝔽₈)) #37528372

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

Aliases

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

	subgroup	G/H
center, Frattini, hypercenter	C₂	C₁₁⋊((C₅⋊D₅)⋊ΓL(1,𝔽₈))
commutator, hypocenter	C₅²×C₇×C₁₁	C₃×C₄
Fitting, socle, cosocle	C₂×C₅²×C₇×C₁₁	C₂×C₃
prime radical	C₂×C₁₁×C₇⋊(C₅²⋊C₃)	C₂
LCS	G ▷ C₅²×C₇×C₁₁
UCS	C₁ ◁ C₂

72 conjugacy classes of subgroups.

μ_t(G) = 4620

Polycyclic presentation:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 183);