C₁₃×#2054 #13111112

order	1664
nilpotency class	3
isoclinism	isoclinic class of #1999
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂⁴

Aliases

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₁₃
prime radical	C₂²×C₁₃×D₈	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

360 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 104 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)(14,15)(16,17)(23,28)(24,29)(25,26);(18,19)(20,21)(22,23)(24,25)(26,28)(27,29);(15,17)(19,21)(22,24,25,23,27,28,26,29)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1664, 786);