C₄₁×#10035 #23786236

order	10496
nilpotency class	3
isoclinism	isoclinic class of #10012
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄₁ · Schur multiplier (H₂) = C₂³

Aliases

	subgroup	G/H
center	C₂×C₄×C₄₁	#127
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₄₁
socle	C₂²×C₄₁	#392
prime radical	C₄₁×#532	C₂²
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₄₁ ◁ C₂×C₄²×C₄₁ ◁ G

498 conjugacy classes of subgroups.

1640 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10496, 3023);