C₂×C₁₃×#394 #13111444

order	1664
nilpotency class	2
isoclinism	isoclinic class of #392
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₃ · Schur multiplier (H₂) = C₂⁷

Aliases

C₂×C₁₃×#394

	subgroup	G/H
center, socle	C₂⁴×C₁₃	C₂³
commutator, Frattini, cosocle	C₂³	C₂⁴×C₁₃
prime radical	C₂³×D₄×C₁₃	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₃ ◁ G

1252 conjugacy classes of subgroups.

minimal degree	μ(G) = 27
transitive degree	μ_t(G) = 832

A minimal faithful permutation representation — 4 generators on 27 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1664, 1118);