Finite Group Databasebeta

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C₂×C₄₁×#1453 #23793522

order	10496
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄²×C₄₁ · Schur multiplier (H₂) = C₂³×C₈

Aliases

C₂×C₄₁×#1453

Subgroups

	subgroup	G/H
center	C₂×C₄²×C₄₁	C₂³
commutator	C₂²	C₂²×C₄²×C₄₁
Frattini, cosocle	C₄²	C₂⁴×C₄₁
socle	C₂³×C₄₁	C₂×C₄²
prime radical	C₂⁴×C₄₁	C₄²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄²×C₄₁ ◁ G

866 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

4592 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10496, 10309);