C₂×C₁₃×#550 #13112525

order	1664
nilpotency class	2
isoclinism	isoclinic class of D₄²
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₁₃ · Schur multiplier (H₂) = C₂⁹

Aliases

C₂×C₁₃×#550

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

1736 conjugacy classes of subgroups.

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1664, 2199);