#35215702

order	20864
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂³

Aliases

No aliases for this group.

C₁₆₃ ⋊ #2030

	subgroup	G/H
center	C₂²	#19104704
commutator, prime radical, cosocle	C₂⁴×C₁₆₃	C₂³
Frattini	C₂⁴	C₂²×D₁₆₃
Fitting	#543×C₁₆₃	C₂
socle	C₂²×C₁₆₃	#120
hypercenter	#543	D₁₆₃
hypocenter	C₁₆₃	#2030
LCS	G ▷ C₂⁴×C₁₆₃ ▷ C₂×C₁₆₃ ▷ C₁₆₃
UCS	C₁ ◁ C₂² ◁ C₂⁴ ◁ #543

290 conjugacy classes of subgroups.

μ_t(G) = 5216

Polycyclic presentation:

2^7,163|a^2=d,b^2=d,c^2=g,b^a=bd,c^a=ce,f^a=fg,c^b=cf,e^b=eg,h^c=h^162

1808 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20864, 5676);