#17957414

order	4352
automorphism	?
homology	Abelianization (H₁) = C₂×C₄² · Schur multiplier (H₂) = C₂⁴×C₄

supersolvable
metabelian
solvable
monomial

Aliases

No aliases for this group.

Splittings

Fitting	C₂×C₁₇×C₂²⋊C₈ ⋊ C₄
Sylow	C₁₇ ⋊ #10961

Subgroups

	subgroup	G/H
center	C₂×C₄	C₂×C₂²⋊#595
commutator	C₂³×C₁₇	C₂×C₄²
Frattini	C₂²×C₄	C₂²×#595
Fitting	C₂×C₁₇×C₂²⋊C₈	C₄
socle	C₂²×C₁₇	C₄×C₂²⋊C₄
prime radical	C₂²×#63252	C₂²
cosocle	C₂²×C₄×D₁₇	C₂³
hypercenter	C₂×C₂²⋊C₈	#595
hypocenter	C₁₇	#10961
LCS	G ▷ C₂³×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ C₂×C₂²⋊C₈

926 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 1088

Polycyclic presentation:

2^8,17|a^2=f,b^2=g,c^2=ef,f^2=h,b^a=bd,c^a=ce,d^a=dh,e^a=eh,g^a=gh,i^a=i^4,d^b=dh,e^b=eh,f^b=fh,i^b=i^4,d^c=dh,e^c=eh,f^c=fh,i^c=i^13,i^f=i^16,i^g=i^16

Conjugacy classes & character table

224 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1092658);