#17962897

order	4352
automorphism	?
homology	Abelianization (H₁) = C₂²×C₁₆ · Schur multiplier (H₂) = C₂

Aliases

No aliases for this group.

	subgroup	G/H
center, Frattini	C₂×C₈	C₂²×#595
commutator, socle, prime radical	C₂²×C₁₇	C₂²×C₁₆
Fitting	C₈×Q₈×C₁₇	C₄
cosocle	C₂×#63214	C₂³
hypercenter	C₈×Q₈	#595
hypocenter	C₁₇	#13660
LCS	G ▷ C₂²×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₈ ◁ C₈×Q₈

158 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 158 conjugacy classes of subgroups — too many to draw. Only its 100 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=d,c^2=de,e^2=f,f^2=g,g^2=h,b^a=bd,c^a=ch,i^a=i^13,i^c=i^13,i^e=i^16

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1098141);