#31797204

order	17536
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈ · Schur multiplier (H₂) = C₂

Aliases

No aliases for this group.

C₁₃₇ ⋊ #2183

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×#10587739
commutator, socle, prime radical	C₂²×C₁₃₇	C₂²×C₈
Fitting	C₄×Q₈×C₁₃₇	C₄
cosocle	C₂×#11764040	C₂³
hypercenter	C₄×Q₈	#10587739
hypocenter	C₁₃₇	#2183
LCS	G ▷ C₂²×C₁₃₇ ▷ C₁₃₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄×Q₈

126 conjugacy classes of subgroups.

μ_t(G) = 17536

Polycyclic presentation:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17536, 20925);