C₅₃×#3483 #20272420

order	6784
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₅₃ · Schur multiplier (H₂) = C₂⁸

Aliases

	subgroup	G/H
center	C₂×C₄×C₅₃	C₂⁴
commutator, Frattini, cosocle	C₂²	C₂⁵×C₅₃
socle	C₂²×C₅₃	C₂⁵
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅₃ ◁ G

1202 conjugacy classes of subgroups; only the 800 normal subgroups are shown.

normal subgroups only

This group has 1202 conjugacy classes of subgroups — too many to draw. Only its 800 normal subgroups are shown.

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

2650 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6784, 2215);