#16954099

order	4352
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂²

Aliases

No aliases for this group.

Splittings

Sylow

C₁₇ ⋊ #13477

Subgroups

	subgroup	G/H
center	C₂³	D₈×D₁₇
commutator, cosocle	C₂²×C₈×C₁₇	C₂³
Frattini	C₂²×C₈	C₂²×D₁₇
Fitting	C₁₇×#1380	C₂
socle, prime radical	C₂³×C₁₇	C₂×D₈
hypercenter	#1380	D₁₇
hypocenter	C₁₇	#13477
LCS	G ▷ C₂²×C₈×C₁₇ ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ #1380

346 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 4352

Polycyclic presentation:

2^8,17|a^2=de,b^2=dgh,c^2=h,d^2=gh,e^2=g,f^2=g,g^2=h,b^a=bd,c^a=ce,d^a=dg,e^a=egh,f^a=fgh,g^a=gh,i^a=i^16,c^b=cf,i^b=i^16,d^c=dg,e^c=egh,f^c=fgh,g^c=gh,i^c=i^16

Conjugacy classes & character table

404 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 89343);