C₁₃×#2397 #13111455

order	1664
nilpotency class	2
isoclinism	isoclinic class of #392
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₃ · Schur multiplier (H₂) = C₂⁶

Aliases

	subgroup	G/H
center	C₂²×C₄×C₁₃	C₂³
commutator, Frattini, cosocle	C₂³	C₂⁴×C₁₃
socle	C₂³×C₁₃	C₂⁴
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₃ ◁ G

840 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 4 generators on 29 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1664, 1129);