C₁₁⋊(ΓL(1,𝔽₈)⋊#1035) #37528243

order	23100
automorphism	?
homology	Abelianization (H₁) = C₃×C₄ · Schur multiplier (H₂) = C₁

Aliases

unambiguous semidirect product	C₁₁⋊(ΓL(1,𝔽₈)⋊#1035)
unambiguous semidirect product	ΓL(1,𝔽₈)⋊(C₁₁⋊#1035)
unambiguous semidirect product	(C₇⋊(C₁₁⋊#1035))⋊C₃

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, hypocenter	C₇×C₁₁×C₂₅	C₃×C₄
Frattini	C₅	C₁₁⋊(ΓL(1,𝔽₈)⋊AGL(1,𝔽₅))
socle	C₅×C₇×C₁₁	C₃×AGL(1,𝔽₅)
prime radical	C₁₁×ΓL(1,𝔽₈)×D₂₅	C₂
cosocle	C₇×C₁₁×D₂₅	C₂×C₃
LCS	G ▷ C₇×C₁₁×C₂₅
UCS	C₁

72 conjugacy classes of subgroups.

μ_t(G) = 1925

Polycyclic presentation:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 54);