C₂×C₃×SD₁₆×C₁₉ #14269811

order	1824
nilpotency class	3
isoclinism	isoclinic class of D₈
automorphism	?
homology	Abelianization (H₁) = C₂³×C₃×C₁₉ · Schur multiplier (H₂) = C₂²

Aliases

C₂×C₃×SD₁₆×C₁₉

	subgroup	G/H
center, socle	C₂²×C₃×C₁₉	D₄
commutator, Frattini, cosocle	C₄	C₂³×C₃×C₁₉
prime radical	C₂×C₃×D₄×C₁₉	C₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₁₉ ◁ C₂×C₃×C₄×C₁₉ ◁ G

136 conjugacy classes of subgroups.

minimal degree	μ(G) = 32
transitive degree	μ_t(G) = 912

A minimal faithful permutation representation — 3 generators on 32 points:

(1,2)(11,12,13)(14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32);(3,4,5,6,7,8,9,10);(4,6)(5,9)(8,10)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1824, 1038);