C₂₉×C₄⋊#401 #20310054

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

Aliases

direct product	C₂₉×C₄⋊#401
unambiguous semidirect product	C₄⋊(C₂₉×#401)

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

1106 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, 8142);