#31796718

order	17536
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂²

Aliases

No aliases for this group.

C₁₃₇ ⋊ #1840

	subgroup	G/H
center, Frattini	C₂³	C₂²×#10587739
commutator, socle, prime radical	C₂³×C₁₃₇	C₂²×C₄
Fitting	#95×C₁₃₇	C₄
cosocle	C₂²×Dic₁₃₇	C₂³
hypercenter	#95	#10587739
hypocenter	C₁₃₇	#1840
LCS	G ▷ C₂³×C₁₃₇ ▷ C₁₃₇
UCS	C₁ ◁ C₂³ ◁ #95

196 conjugacy classes of subgroups.

μ_t(G) = 17536

Polycyclic presentation:

2^7,137|a^2=f,b^2=de,c^2=d,f^2=g,b^a=bd,c^a=ce,h^a=h^100,c^b=cg,h^f=h^136

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17536, 20439);