#16953226

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

Aliases

No aliases for this group.

Splittings

Sylow

C₁₇ ⋊ #13337

Subgroups

	subgroup	G/H
center	C₂²	#11762941
commutator, cosocle	C₂²×C₈×C₁₇	C₂³
Frattini	C₂²×C₈	C₂²×D₁₇
Fitting, prime radical	C₂×C₁₇×#509	C₂
socle	C₂²×C₁₇	#447
hypercenter	C₂×#509	D₁₇
hypocenter	C₁₇	#13337
LCS	G ▷ C₂²×C₈×C₁₇ ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#509

554 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 554 conjugacy classes of subgroups — too many to draw. Only its 101 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 1088

Polycyclic presentation:

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

Conjugacy classes & character table

296 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 88470);