C₂₉×C₂²⋊#401 #20309727

order	7424
nilpotency class	2
isoclinism	isoclinic class of #14715
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₂₉ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product	C₂₉×C₂²⋊#401
unambiguous semidirect product	C₂²⋊(C₂₉×#401)

	subgroup	G/H
center, socle	C₂⁴×C₂₉	C₂⁴
commutator, Frattini, cosocle	C₂⁴	C₂⁴×C₂₉
prime radical	C₂⁵×C₂₉	C₂³
LCS	G ▷ C₂⁴ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₂₉ ◁ G

1650 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, 7815);