C₁₉×#123 #10597409

order	608
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂²

Aliases

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

78 conjugacy classes of subgroups.

minimal degree	μ(G) = 31
transitive degree	μ_t(G) = 304

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);(24,25)(26,29)(27,28)(30,31);(20,21)(22,23)(24,26,27,30)(25,29,28,31)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(608, 158);