#30597965

order	15616
automorphism	?
homology	Abelianization (H₁) = C₂×C₄² · Schur multiplier (H₂) = C₂×C₄

Aliases

No aliases for this group.

C₆₁ ⋊ #8263

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×#6923
commutator, socle, prime radical	C₂³×C₆₁	C₂×C₄²
Fitting	C₂×#97×C₆₁	C₄
cosocle	C₂×C₄×Dic₆₁	C₂³
hypercenter	C₂×#97	#6923
hypocenter	C₆₁	#8263
LCS	G ▷ C₂³×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×#97

470 conjugacy classes of subgroups.

μ_t(G) = 15616

Polycyclic presentation:

2^8,61|a^2=e,b^2=f,c^2=de,e^2=g,f^2=h,b^a=bd,c^a=cg,c^b=ch,i^b=i^11,i^f=i^60

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 1087520);