C₂₉×#10605 #20305505

order	7424
nilpotency class	3
isoclinism	isoclinic class of #10603
automorphism	?
homology	Abelianization (H₁) = C₂³×C₂₉ · Schur multiplier (H₂) = C₂

Aliases

	subgroup	G/H
center, socle	C₂²×C₂₉	#396
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₂₉
prime radical	C₂³×C₂₉	C₂²⋊Q₈
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₂₉ ◁ C₂×C₄²×C₂₉ ◁ G

306 conjugacy classes of subgroups.

1073 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7424, 3593);