C₁₉×#6860 #17987246

order	4617
nilpotency class	3
isoclinism	isoclinic class of #6856
automorphism	?
homology	Abelianization (H₁) = C₃²×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

	subgroup	G/H
center, socle	C₃²×C₁₉	H(3,𝔽₃)
commutator, Frattini, cosocle	C₃³	C₃²×C₁₉
prime radical	C₃³×C₁₉	C₃²
LCS	G ▷ C₃³ ▷ C₃² ▷ C₁
UCS	C₁ ◁ C₃²×C₁₉ ◁ C₃³×C₁₉ ◁ G

70 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 2 generators on 37 points:

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4617, 7);