#17973562

order	4352
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁴

Aliases

No aliases for this group.

	subgroup	G/H
center, Frattini	C₂³	C₂³×#595
commutator, socle, prime radical	C₂³×C₁₇	C₂³×C₄
Fitting	C₂×C₁₇×C₄⋊Q₈	C₄
cosocle	C₂²×Dic₁₇	C₂⁴
hypercenter	C₂×C₄⋊Q₈	#595
hypocenter	C₁₇	#22242
LCS	G ▷ C₂³×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄⋊Q₈

722 conjugacy classes of subgroups; only the 224 normal subgroups are shown.

normal subgroups only

This group has 722 conjugacy classes of subgroups — too many to draw. Only its 224 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=g,b^2=g,c^2=ef,d^2=e,g^2=h,b^a=be,c^a=cf,d^a=deh,i^a=i^4,c^b=ceh,i^b=i^13,i^c=i^16,i^d=i^16,i^g=i^16

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1108806);