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#29721514

order	15616
automorphism	?
homology	Abelianization (H₁) = C₂⁴ · Schur multiplier (H₂) = C₂⁴

Aliases

No aliases for this group.

Splittings

C₆₁ ⋊ #24724

Subgroups

	subgroup	G/H
center	C₂²	C₂×#14519749
commutator, cosocle	C₂²×C₄×C₆₁	C₂⁴
Frattini	C₂²×C₄	C₂³×D₆₁
Fitting	C₄×AGL(1,ℤ/8)×C₆₁	C₂
socle	C₂²×C₆₁	C₂×#121
prime radical	C₂×AGL(1,ℤ/8)×C₆₁	C₂²
hypercenter	C₄×AGL(1,ℤ/8)	D₆₁
hypocenter	C₆₁	#24724
LCS	G ▷ C₂²×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₄×AGL(1,ℤ/8)

690 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 3904

Polycyclic presentation:

2^8,61|a^2=ef,d^2=eh,f^2=h,g^2=h,b^a=be,c^a=cf,d^a=de,i^a=i^60,c^b=cg,g^b=gh,f^c=fh,g^c=gh

Conjugacy classes & character table

1363 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 211069);