#29688320

order	15616
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂³

Aliases

No aliases for this group.

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₆₁
commutator, socle, prime radical	C₂³×C₆₁	C₂³×C₄
Fitting	C₆₁×#1916	C₂
cosocle	C₂²×C₄×C₆₁	C₂⁴
hypercenter	#1916	D₆₁
hypocenter	C₆₁	#21673
LCS	G ▷ C₂³×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂²×C₄ ◁ #1916

694 conjugacy classes of subgroups.

μ_t(G) = 15616

Polycyclic presentation:

2^8,61|a^2=g,b^2=f,c^2=e,d^2=eg,g^2=h,b^a=be,c^a=cf,d^a=dh,i^c=i^60,i^d=i^60

1768 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 177875);