#29571167

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

Aliases

No aliases for this group.

C₆₁ ⋊ #8265

	subgroup	G/H
center, Frattini	C₂×C₄²	C₂²×D₆₁
commutator, socle, prime radical	C₂³×C₆₁	C₂×C₄²
Fitting	C₄×C₄⋊C₈×C₆₁	C₂
cosocle	C₂×C₄²×C₆₁	C₂³
hypercenter	C₄×C₄⋊C₈	D₆₁
hypocenter	C₆₁	#8265
LCS	G ▷ C₂³×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₄² ◁ C₄×C₄⋊C₈

438 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=ch,i^a=i^60,c^b=cg,i^c=i^60

2488 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 60722);