#30639896

order	16256
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂³

Aliases

No aliases for this group.

C₁₂₇ ⋊ #2030

	subgroup	G/H
center	C₂²	#16861178
commutator, prime radical, cosocle	C₂⁴×C₁₂₇	C₂³
Frattini	C₂⁴	C₂²×D₁₂₇
Fitting	#543×C₁₂₇	C₂
socle	C₂²×C₁₂₇	#120
hypercenter	#543	D₁₂₇
hypocenter	C₁₂₇	#2030
LCS	G ▷ C₂⁴×C₁₂₇ ▷ C₂×C₁₂₇ ▷ C₁₂₇
UCS	C₁ ◁ C₂² ◁ C₂⁴ ◁ #543

290 conjugacy classes of subgroups.

Polycyclic presentation:

2^7,127|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^126

1412 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16256, 5676);