#17062459

order	4352
automorphism	?
homology	Abelianization (H₁) = C₂⁴ · Schur multiplier (H₂) = C₂⁵

Aliases

No aliases for this group.

	subgroup	G/H
center	C₂×C₄	#10587568
commutator, prime radical, cosocle	C₂⁴×C₁₇	C₂⁴
Frattini	C₂⁴	C₂³×D₁₇
Fitting	C₁₇×#1740	C₂
socle	C₂²×C₁₇	C₂×#120
hypercenter	#1740	D₁₇
hypocenter	C₁₇	#23564
LCS	G ▷ C₂⁴×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ #1740

1162 conjugacy classes of subgroups.

μ_t(G) = 1088

Polycyclic presentation:

2^8,17|a^2=e,b^2=e,c^2=e,d^2=h,b^a=be,c^a=cf,g^a=gh,c^b=cg,f^b=fh,i^b=i^16,i^c=i^16

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 197703);