C₁₃×#1629 #13110687

order	1664
nilpotency class	3
isoclinism	isoclinic class of #1619
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂³

Aliases

	subgroup	G/H
center, socle	C₂²×C₁₃	#120
commutator, Frattini, cosocle	C₄²	C₂³×C₁₃
prime radical	D₄²×C₁₃	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₄²×C₁₃ ◁ G

314 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 76 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) = 416

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1664, 361);