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#29575496

order	15616
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂³

Aliases

No aliases for this group.

Splittings

C₆₁ ⋊ #9097

Subgroups

	subgroup	G/H
center	C₂×C₄	#14519749
commutator	C₂²×C₄×C₆₁	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₆₁
Fitting	C₄×AGL(1,ℤ/8)×C₆₁	C₂
socle	C₂²×C₆₁	#386
prime radical	C₂×AGL(1,ℤ/8)×C₆₁	C₄
cosocle	C₂×C₄²×C₆₁	C₂³
hypercenter	C₄×AGL(1,ℤ/8)	D₆₁
hypocenter	C₆₁	#9097
LCS	G ▷ C₂²×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₄×AGL(1,ℤ/8)

520 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 3904

Polycyclic presentation:

2^8,61|a^2=f,b^2=df,e^2=g,f^2=h,b^a=bd,c^a=ce,d^a=dg,i^a=i^60,c^b=ch,d^b=dg,e^b=eg,f^b=fg,i^b=i^60,d^c=dg,e^c=eg,f^c=fg

Conjugacy classes & character table

1372 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 65051);