C₄₁×#13698 #23789899

order	10496
nilpotency class	5
isoclinism	isoclinic class of #13697
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄₁ · Schur multiplier (H₂) = C₂²

Aliases

	subgroup	G/H
center, socle	C₂²×C₄₁	C₂×D₁₆
commutator, Frattini, cosocle	C₂×C₁₆	C₂³×C₄₁
prime radical	C₂³×C₄₁	D₁₆
LCS	G ▷ C₂×C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄₁ ◁ C₂²×C₄×C₄₁ ◁ C₂²×C₈×C₄₁ ◁ C₂²×C₁₆×C₄₁ ◁ G

190 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 190 conjugacy classes of subgroups — too many to draw. Only its 74 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

1886 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10496, 6686);