C₂₉×#60562 #20355462

order	7424
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₂₉ · Schur multiplier (H₂) = C₂⁸

Aliases

	subgroup	G/H
center	C₂×C₄×C₂₉	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₉
socle	C₂²×C₂₉	C₂³×D₄
prime radical	C₂²×#41×C₂₉	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₉ ◁ C₂²×C₄²×C₂₉ ◁ G

2148 conjugacy classes of subgroups.

1856 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7424, 53550);