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C₄×C₂₉×#410 #20315291

order	7424
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄²×C₂₉ · Schur multiplier (H₂) = C₂⁴×C₄²

Aliases

C₄×C₂₉×#410

Subgroups

	subgroup	G/H
center	C₄²×C₂₉	C₂²⋊C₄
commutator	C₂²	C₂²×C₄²×C₂₉
Frattini, cosocle	C₂⁴	C₂⁴×C₂₉
socle	C₂²×C₂₉	C₂²×C₂²⋊C₄
prime radical	C₂²×#41×C₂₉	C₂²
LCS	G ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄²×C₂₉ ◁ C₂²×C₄²×C₂₉ ◁ G

1666 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2552 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7424, 13379);