ΓL(1,𝔽₈)⋊#13133334 #49087664

order	35700
automorphism	?
homology	Abelianization (H₁) = C₃×C₄ · Schur multiplier (H₂) = C₅

Aliases

	subgroup	G/H
center, Frattini, hypercenter	C₂	C₅⋊(C₅⋊(C₁₇⋊AGL(1,𝔽₇)))
commutator, hypocenter	C₅²×C₇×C₁₇	C₃×C₄
Fitting, socle, cosocle	C₂×C₅²×C₇×C₁₇	C₂×C₃
prime radical	C₂×C₅²×C₁₇×ΓL(1,𝔽₈)	C₂
LCS	G ▷ C₅²×C₇×C₁₇
UCS	C₁ ◁ C₂

192 conjugacy classes of subgroups.

μ_t(G) = 11900

Polycyclic presentation:

2,3,5^2,7,17,2|a^2=g,c^a=c^4,d^a=d^4,e^a=e^6,f^a=f^16,e^b=e^2

2134 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35700, 138);