#31780934

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	C₂²×C₄	C₂²×D₁₃₇
commutator, socle, prime radical	C₂³×C₁₃₇	C₂²×C₄
Fitting	#376×C₁₃₇	C₂
cosocle	C₂²×C₄×C₁₃₇	C₂³
hypercenter	#376	D₁₃₇
hypocenter	C₁₃₇	#1840
LCS	G ▷ C₂³×C₁₃₇ ▷ C₁₃₇
UCS	C₁ ◁ C₂²×C₄ ◁ #376

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^136,c^b=cg

2764 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17536, 4655);