C₄₁×#62694 #23838895

order	10496
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂⁶×C₄₁ · Schur multiplier (H₂) = C₂¹³

Aliases

	subgroup	G/H
center	C₄²×C₄₁	C₂⁴
commutator, Frattini, cosocle	C₂²	C₂⁶×C₄₁
socle	C₂²×C₄₁	C₂⁶
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₄²×C₄₁ ◁ G

6640 conjugacy classes of subgroups; only the 5670 normal subgroups are shown.

normal subgroups only

This group has 6640 conjugacy classes of subgroups — too many to draw. Only its 5670 normal subgroups are shown.

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

3116 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10496, 55682);