C₂×C₄₇×H(3,𝔽₄) #20241136

order	6016
nilpotency class	2
isoclinism	isoclinic class of #560
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₄₇ · Schur multiplier (H₂) = C₂⁶×C₄²

Aliases

	subgroup	G/H
center, socle	C₂³×C₄₇	C₂⁴
commutator, Frattini, cosocle	C₂²	C₂⁵×C₄₇
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₄₇ ◁ G

1408 conjugacy classes of subgroups.

1786 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6016, 2258);