C₁₃×#2091 #13111149

order	1664
nilpotency class	3
isoclinism	isoclinic class of #2010
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂²

Aliases

	subgroup	G/H
center	C₄×C₁₃	#127
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₁₃
socle	C₂×C₁₃	#399
prime radical	C₂⁴×C₁₃	Q₈
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ G

222 conjugacy classes of subgroups.

minimal degree	μ(G) = 29
transitive degree	μ_t(G) = 208

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1664, 823);