C₃⋊(C₇⋊(C₁₁⋊#1035)) #37528287

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

Aliases

unambiguous semidirect product	C₃⋊(C₇⋊(C₁₁⋊#1035))
unambiguous semidirect product	C₇⋊(C₃⋊(C₁₁⋊#1035))
unambiguous semidirect product	C₁₁⋊(C₃⋊(C₇⋊#1035))

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

72 conjugacy classes of subgroups.

μ_t(G) = 5775

Polycyclic presentation:

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

1620 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 98);