C₁₃×#1686 #13110744

order	1664
nilpotency class	3
isoclinism	isoclinic class of #1685
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂

Aliases

	subgroup	G/H
center, socle	C₂²×C₁₃	#121
commutator, Frattini, cosocle	C₄²	C₂³×C₁₃
prime radical	C₁₃×#127	C₂²
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₄²×C₁₃ ◁ G

168 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 168 conjugacy classes of subgroups — too many to draw. Only its 68 normal subgroups are shown.

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

minimal degree	μ(G) = 29
transitive degree	μ_t(G) = 832

A minimal faithful permutation representation — 3 generators on 29 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13)(15,18)(16,20)(19,21)(23,26)(24,28)(27,29);(14,15,16,18,17,19,20,21);(15,19)(18,21)(22,23,25,27)(24,29,28,26)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1664, 418);