#29599772

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

Aliases

No aliases for this group.

Splittings

Sylow

C₆₁ ⋊ #13475

Subgroups

	subgroup	G/H
center	C₂³	C₂×D₄₈₈
commutator, cosocle	C₂²×C₈×C₆₁	C₂³
Frattini	C₂²×C₈	C₂²×D₆₁
Fitting	C₂×C₆₁×C₄⋊C₁₆	C₂
socle, prime radical	C₂³×C₆₁	C₂×D₈
hypercenter	C₂×C₄⋊C₁₆	D₆₁
hypocenter	C₆₁	#13475
LCS	G ▷ C₂²×C₈×C₆₁ ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×C₄⋊C₁₆

346 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 15616

Polycyclic presentation:

2^8,61|a^2=de,b^2=dg,c^2=h,d^2=gh,e^2=g,f^2=g,g^2=h,b^a=bd,c^a=ce,d^a=dg,e^a=egh,f^a=fgh,g^a=gh,i^a=i^60,c^b=cf,d^c=dg,e^c=egh,f^c=fgh,g^c=gh,i^c=i^60

Conjugacy classes & character table

2452 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 89327);