ΓL(1,𝔽₈)⋊(Dic₁₁⋊C₂₅) #37528225

order	23100
automorphism	?
homology	Abelianization (H₁) = C₃×C₄×C₂₅ · Schur multiplier (H₂) = C₁

Aliases

unambiguous semidirect product	ΓL(1,𝔽₈)⋊(Dic₁₁⋊C₂₅)
unambiguous semidirect product	(C₁₁⋊C₂₅)⋊(ΓL(1,𝔽₈)⋊C₄)
unambiguous semidirect product	(C₁₁⋊(ΓL(1,𝔽₈)⋊C₄))⋊C₂₅
unambiguous semidirect product	(C₇⋊(Dic₁₁⋊C₂₅))⋊C₃

	subgroup	G/H
center, Frattini, hypercenter	C₂×C₅	ΓL(1,𝔽₈)⋊AGL(1,𝔽₁₁)
commutator, hypocenter	C₇×C₁₁	C₃×C₄×C₂₅
Fitting, socle, cosocle	C₂×C₅×C₇×C₁₁	C₂×C₃×C₅
prime radical	C₂×C₅×C₁₁×ΓL(1,𝔽₈)	C₂×C₅
LCS	G ▷ C₇×C₁₁
UCS	C₁ ◁ C₂×C₅

72 conjugacy classes of subgroups.

μ_t(G) = 7700

Polycyclic presentation:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 36);