C₂×C₁₃×#525 #13112493

order	1664
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₁₃ · Schur multiplier (H₂) = C₂⁹

Aliases

C₂×C₁₃×#525

	subgroup	G/H
center	C₂²×C₄×C₁₃	C₂³
commutator, Frattini, cosocle	C₂²	C₂⁵×C₁₃
socle	C₂³×C₁₃	C₂⁴
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₃ ◁ G

1880 conjugacy classes of subgroups.

minimal degree	μ(G) = 27
transitive degree	μ_t(G) = 416

A minimal faithful permutation representation — 5 generators on 27 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1664, 2167);