C₂×C₁₃×#2091 #15710061

order	3328
nilpotency class	3
isoclinism	isoclinic class of #2010
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₃ · Schur multiplier (H₂) = C₂⁵

Aliases

	subgroup	G/H
center	C₂×C₄×C₁₃	#127
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
socle	C₂²×C₁₃	#399
prime radical	C₂⁵×C₁₃	Q₈
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ C₂³×C₄×C₁₃ ◁ G

1102 conjugacy classes of subgroups.

minimal degree	μ(G) = 31
transitive degree	μ_t(G) = 416

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);(3,4,6,10,7,9,12,16)(5,11,13,17,14,18,15,8);(3,5,12,13,7,14,6,15)(4,8,16,11,9,17,10,18);(4,9)(10,16)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 16710);