C₁₁⋊(ΓL(1,𝔽₈)⋊Dic₁₇) #30628103

order	15708
automorphism	?
homology	Abelianization (H₁) = C₃×C₄ · Schur multiplier (H₂) = C₁

Aliases

unambiguous semidirect product	C₁₁⋊(ΓL(1,𝔽₈)⋊Dic₁₇)
unambiguous semidirect product	ΓL(1,𝔽₈)⋊Dic₁₈₇
unambiguous semidirect product	Dic₁₃₀₉⋊C₃

	subgroup	G/H
center, Frattini, hypercenter	C₂	C₁₁⋊(C₁₇⋊AGL(1,𝔽₇))
commutator, hypocenter	C₇×C₁₁×C₁₇	C₃×C₄
Fitting, socle, cosocle	C₂×C₇×C₁₁×C₁₇	C₂×C₃
prime radical	C₂×C₁₁×C₁₇×ΓL(1,𝔽₈)	C₂
LCS	G ▷ C₇×C₁₁×C₁₇
UCS	C₁ ◁ C₂

48 conjugacy classes of subgroups.

μ_t(G) = 5236

Polycyclic presentation:

2,3,7,11,17,2|a^2=f,c^a=c^6,d^a=d^10,e^a=e^16,c^b=c^2

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15708, 24);