Finite Group Databasebeta

← Prev (#23796566) Next (#23796568) →

C₄₁×#20366 #23796567

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

Aliases

C₄₁×#20366

Subgroups

	subgroup	G/H
center	C₂×C₄²×C₄₁	C₂³
commutator	C₂²	C₂²×C₄²×C₄₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
socle	C₂³×C₄₁	C₂³×C₄
prime radical	C₂⁴×C₄₁	C₂²×C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄²×C₄₁ ◁ G

1078 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, 13354);