C₂×C₁₃×#535 #13112504

order	1664
nilpotency class	2
isoclinism	isoclinic class of #534
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₁₃ · Schur multiplier (H₂) = C₂⁸×C₄

Aliases

C₂×C₁₃×#535

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

1896 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);(4,6)(8,11)(9,13);(7,8,10,11)(9,12,13,14);(3,4)(5,6)(7,8)(9,12)(10,11)(13,14);(7,9)(8,12)(10,13)(11,14)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1664, 2178);