#45665486

order	32896
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂³

Aliases

No aliases for this group.

C₂₅₇ ⋊ #2030

	subgroup	G/H
center	C₂²	#22551561
commutator, prime radical, cosocle	C₂⁴×C₂₅₇	C₂³
Frattini	C₂⁴	C₂²×D₂₅₇
Fitting	#543×C₂₅₇	C₂
socle	C₂²×C₂₅₇	#120
hypercenter	#543	D₂₅₇
hypocenter	C₂₅₇	#2030
LCS	G ▷ C₂⁴×C₂₅₇ ▷ C₂×C₂₅₇ ▷ C₂₅₇
UCS	C₁ ◁ C₂² ◁ C₂⁴ ◁ #543

290 conjugacy classes of subgroups.

μ_t(G) = 8224

Polycyclic presentation:

2^7,257|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^256

2842 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32896, 5676);