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C₃₁×#20472 #21477231

order	7936
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄²×C₃₁ · Schur multiplier (H₂) = C₂²×C₄²

Aliases

C₃₁×#20472

Subgroups

	subgroup	G/H
center	C₂×C₄²×C₃₁	C₂³
commutator	C₂²	C₂²×C₄²×C₃₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₁
socle	C₂³×C₃₁	C₂³×C₄
prime radical	C₂⁴×C₃₁	C₂²×C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄²×C₃₁ ◁ G

1050 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3472 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7936, 13460);