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C₄×C₃₁×#410 #21477150

order	7936
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄²×C₃₁ · Schur multiplier (H₂) = C₂⁴×C₄²

Aliases

C₄×C₃₁×#410

Subgroups

	subgroup	G/H
center	C₄²×C₃₁	C₂²⋊C₄
commutator	C₂²	C₂²×C₄²×C₃₁
Frattini, cosocle	C₂⁴	C₂⁴×C₃₁
socle	C₂²×C₃₁	C₂²×C₂²⋊C₄
prime radical	C₂²×#41×C₃₁	C₂²
LCS	G ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄²×C₃₁ ◁ C₂²×C₄²×C₃₁ ◁ G

1666 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2728 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7936, 13379);