#17039014

order	4352
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂²×C₄

Aliases

No aliases for this group.

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₁₇
commutator, socle, prime radical	C₂³×C₁₇	C₂³×C₄
Fitting	C₁₇×#1917	C₂
cosocle	C₂²×C₄×C₁₇	C₂⁴
hypercenter	#1917	D₁₇
hypocenter	C₁₇	#21340
LCS	G ▷ C₂³×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂²×C₄ ◁ #1917

766 conjugacy classes of subgroups.

μ_t(G) = 4352

Polycyclic presentation:

2^8,17|a^2=g,b^2=fg,c^2=f,d^2=e,g^2=h,b^a=be,c^a=cf,c^b=ch,i^c=i^16,i^d=i^16

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 174258);