#31807570

order	17792
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂³

Aliases

No aliases for this group.

C₁₃₉ ⋊ #2030

	subgroup	G/H
center	C₂²	#17984811
commutator, prime radical, cosocle	C₂⁴×C₁₃₉	C₂³
Frattini	C₂⁴	C₂²×D₁₃₉
Fitting	#543×C₁₃₉	C₂
socle	C₂²×C₁₃₉	#120
hypercenter	#543	D₁₃₉
hypocenter	C₁₃₉	#2030
LCS	G ▷ C₂⁴×C₁₃₉ ▷ C₂×C₁₃₉ ▷ C₁₃₉
UCS	C₁ ◁ C₂² ◁ C₂⁴ ◁ #543

290 conjugacy classes of subgroups.

μ_t(G) = 4448

Polycyclic presentation:

2^7,139|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^138

1544 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17792, 5676);