#16924759

order	4352
automorphism	?
homology	Abelianization (H₁) = C₂×C₄² · Schur multiplier (H₂) = C₂³

Aliases

No aliases for this group.

C₁₇ ⋊ #8135

	subgroup	G/H
center, Frattini	C₂×C₄²	C₂²×D₁₇
commutator, socle, prime radical	C₂³×C₁₇	C₂×C₄²
Fitting	C₁₇×#1744	C₂
cosocle	C₂×C₄²×C₁₇	C₂³
hypercenter	#1744	D₁₇
hypocenter	C₁₇	#8135
LCS	G ▷ C₂³×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₄² ◁ #1744

382 conjugacy classes of subgroups; only the 179 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 179 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

μ_t(G) = 4352

Polycyclic presentation:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 60003);