D₄×Q₃₂×C₄₁ #23810053

order	10496
nilpotency class	4
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₄₁ · Schur multiplier (H₂) = C₂⁵

Aliases

D₄×Q₃₂×C₄₁

	subgroup	G/H
center, socle	C₂²×C₄₁	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₄₁
prime radical	C₂×D₄×C₄₁	D₈
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄₁ ◁ C₄×D₄×C₄₁ ◁ C₈×D₄×C₄₁ ◁ G

664 conjugacy classes of subgroups.

2255 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10496, 26840);