#36369497

order	22144
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂³

Aliases

No aliases for this group.

C₁₇₃ ⋊ #1843

	subgroup	G/H
center, Frattini	C₂³	C₂²×#10621924
commutator, socle, prime radical	C₂³×C₁₇₃	C₂²×C₄
Fitting	#95×C₁₇₃	C₄
cosocle	C₂²×Dic₁₇₃	C₂³
hypercenter	#95	#10621924
hypocenter	C₁₇₃	#1843
LCS	G ▷ C₂³×C₁₇₃ ▷ C₁₇₃
UCS	C₁ ◁ C₂³ ◁ #95

256 conjugacy classes of subgroups.

μ_t(G) = 22144

Polycyclic presentation:

2^7,173|a^2=f,b^2=d,c^2=e,f^2=g,b^a=bd,c^a=ce,h^a=h^80,c^b=cg,h^f=h^172

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22144, 20444);