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C₄×C₄₁×#410 #23796592

order	10496
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄²×C₄₁ · Schur multiplier (H₂) = C₂⁴×C₄²

Aliases

C₄×C₄₁×#410

Subgroups

	subgroup	G/H
center	C₄²×C₄₁	C₂²⋊C₄
commutator	C₂²	C₂²×C₄²×C₄₁
Frattini, cosocle	C₂⁴	C₂⁴×C₄₁
socle	C₂²×C₄₁	C₂²×C₂²⋊C₄
prime radical	C₂²×#41×C₄₁	C₂²
LCS	G ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄²×C₄₁ ◁ C₂²×C₄²×C₄₁ ◁ G

1666 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3608 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10496, 13379);