C₂×C₁₃×#478 #13112130

order	1664
nilpotency class	3
isoclinism	isoclinic class of #447
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₃ · Schur multiplier (H₂) = C₂⁴

Aliases

C₂×C₁₃×#478

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₁₃
prime radical	C₂²×D₄×C₁₃	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

448 conjugacy classes of subgroups.

minimal degree	μ(G) = 31
transitive degree	μ_t(G) = 832

A minimal faithful permutation representation — 4 generators on 31 points:

(1,2)(19,20,21,22,23,24,25,26,27,28,29,30,31);(3,4,6,8)(5,9,10,7)(11,12,13,15)(14,16,18,17);(3,5,6,10)(4,7,8,9)(12,15)(16,17);(12,16)(14,18)(15,17)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1664, 1804);