#16925463

order	4352
automorphism	?
homology	Abelianization (H₁) = C₂×C₄² · Schur multiplier (H₂) = C₂×C₄

Aliases

No aliases for this group.

C₁₇ ⋊ #8263

	subgroup	G/H
center, Frattini	C₂×C₄²	C₂²×D₁₇
commutator, socle, prime radical	C₂³×C₁₇	C₂×C₄²
Fitting	C₄×C₁₇×#97	C₂
cosocle	C₂×C₄²×C₁₇	C₂³
hypercenter	C₄×#97	D₁₇
hypocenter	C₁₇	#8263
LCS	G ▷ C₂³×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₄² ◁ C₄×#97

470 conjugacy classes of subgroups.

μ_t(G) = 4352

Polycyclic presentation:

2^8,17|a^2=e,b^2=f,c^2=de,e^2=g,f^2=h,b^a=bd,c^a=cg,c^b=ch,i^b=i^16

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 60707);