#17949597

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

Aliases

No aliases for this group.

Splittings

Sylow

C₁₇ ⋊ #7531

Subgroups

	subgroup	G/H
center	C₂	#14543916
commutator	C₄×C₈×C₁₇	C₂×C₄
Frattini	C₄×C₈	C₂×#595
Fitting	C₈²×C₁₇	C₄
socle	C₂×C₁₇	#1408
prime radical	#11763186	C₄
cosocle	#11763189	C₂²
hypercenter	C₈²	#595
hypocenter	C₁₇	#7531
LCS	G ▷ C₄×C₈×C₁₇ ▷ C₄²×C₁₇ ▷ C₂×C₄×C₁₇ ▷ C₂²×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ C₄² ◁ C₄×C₈ ◁ C₈²

146 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 544

Polycyclic presentation:

2^8,17|a^2=d,c^2=fg,d^2=h,e^2=gh,f^2=h,b^a=bc,c^a=ce,e^a=ef,f^a=fg,g^a=gh,i^a=i^13,c^b=cfgh,d^b=def,e^b=egh,f^b=fh,i^b=i^16,d^c=dfg,e^d=egh,f^d=fh,i^d=i^16

Conjugacy classes & character table

281 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1084841);