#30595284

order	15616
automorphism	?
homology	Abelianization (H₁) = C₂×C₄ · Schur multiplier (H₂) = C₂×C₄

Aliases

No aliases for this group.

Splittings

Fitting	C₈²×C₆₁ ⋊ C₄
Sylow	C₆₁ ⋊ #7530

Subgroups

	subgroup	G/H
center	C₂	#21460951
commutator	C₄×C₈×C₆₁	C₂×C₄
Frattini	C₄×C₈	C₂×#6923
Fitting	C₈²×C₆₁	C₄
socle	C₂×C₆₁	#1408
prime radical, cosocle	#16840139	C₂²
hypercenter	C₈²	#6923
hypocenter	C₆₁	#7530
LCS	G ▷ C₄×C₈×C₆₁ ▷ C₄²×C₆₁ ▷ C₂×C₄×C₆₁ ▷ C₂²×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ C₄² ◁ C₄×C₈ ◁ C₈²

152 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 1952

Polycyclic presentation:

2^8,61|a^2=d,b^2=h,c^2=fg,e^2=gh,f^2=h,b^a=bc,c^a=ce,e^a=ef,f^a=fg,g^a=gh,i^a=i^11,c^b=cfgh,d^b=def,e^b=egh,f^b=fh,i^b=i^60,d^c=dfg,e^d=egh,f^d=fh,i^d=i^60

Conjugacy classes & character table

985 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 1084839);