C₁₃×SD₁₆×#41 #15747765

order	3328
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₁₃ · Schur multiplier (H₂) = C₂⁸

Aliases

C₁₃×SD₁₆×#41

	subgroup	G/H
center	C₂×C₄×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
socle	C₂²×C₁₃	C₂³×D₄
prime radical	D₄×C₁₃×#41	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ C₄×C₁₃×#41 ◁ G

2116 conjugacy classes of subgroups.

minimal degree	μ(G) = 29
transitive degree	μ_t(G) = 832

A minimal faithful permutation representation — 5 generators on 29 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 54414);