C₁₉×#492 #11926168

order	1216
nilpotency class	3
isoclinism	isoclinic class of #465
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂×C₄

Aliases

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂³×C₁₉
prime radical	C₁₉×#127	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₄²×C₁₉ ◁ G

142 conjugacy classes of subgroups.

minimal degree	μ(G) = 31
transitive degree	μ_t(G) = 608

A minimal faithful permutation representation — 3 generators on 31 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1216, 173);