C₁₉×#6900 #17987286

order	4617
nilpotency class	2
isoclinism	isoclinic class of C₃²⋊H(3,𝔽₃)
automorphism	?
homology	Abelianization (H₁) = C₃³×C₁₉ · Schur multiplier (H₂) = C₃

Aliases

	subgroup	G/H
center, socle	C₃²×C₁₉	C₃³
commutator, Frattini, cosocle	C₃²	C₃³×C₁₉
prime radical	C₃³×C₁₉	C₃²
LCS	G ▷ C₃² ▷ C₁
UCS	C₁ ◁ C₃²×C₁₉ ◁ G

140 conjugacy classes of subgroups.

minimal degree	μ(G) = 37
transitive degree	μ_t(G) = 1539

A minimal faithful permutation representation — 3 generators on 37 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(21,23,26)(24,28,27)(30,32,35)(33,37,36);(20,21,24,22,23,27,25,26,28);(29,30,33,31,32,36,34,35,37)

969 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4617, 47);