C₁₉×#6861 #17987247

order	4617
nilpotency class	3
isoclinism	isoclinic class of #6856
automorphism	?
homology	Abelianization (H₁) = C₃²×C₁₉ · Schur multiplier (H₂) = C₃

Aliases

direct product

C₁₉×#6861

Subgroups

	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

50 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 73
transitive degree	μ_t(G) = 1539

A minimal faithful permutation representation — 2 generators on 73 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,24)(22,28,32)(23,27,33)(25,34,30)(26,37,31)(29,39,42)(35,45,46)(36,44,41)(38,43,40)(47,48,51,50,53,60,58,64,70)(49,54,65,57,52,61,56,63,59)(55,62,69,67,72,73,68,66,71);(20,22,29,23,30,40,31,41,46)(21,25,35,27,36,39,26,28,38)(24,32,42,33,34,43,37,44,45)(47,49,55)(48,52,62)(50,57,67)(51,59,69)(53,63,72)(54,66,64)(56,68,58)(60,65,73)(61,71,70)

Conjugacy classes & character table

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

Relationships

Fitting subgroup of	C₁₉⋊C₃×#6861, #28353711, #28353718, …
maximal subgroup of	C₃×C₁₉×#6861, C₁₉×#10624585, C₁₉×#10624587, …
maximal normal subgroup of	C₃×C₁₉×#6861, C₁₉×#10624585, C₁₉×#10624587, …
maximal quotient of	C₁₉×#10624450, C₁₉×#10624451, C₁₉×#10624492, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4617, 8);

C19×#6861 #17987247