C₁₉×#6908 #17987294

order	4617
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₃³×C₁₉ · Schur multiplier (H₂) = C₃³

Aliases

direct product

C₁₉×#6908

Subgroups

	subgroup	G/H
center	C₉×C₁₉	H(3,𝔽₃)
commutator, Frattini, cosocle	C₃²	C₃³×C₁₉
socle	C₃×C₁₉	C₃×H(3,𝔽₃)
LCS	G ▷ C₃² ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₉×C₁₉ ◁ C₃×C₉×C₁₉ ◁ G

134 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 46
transitive degree	μ_t(G) = 513

A minimal faithful permutation representation — 3 generators on 46 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,24)(22,26,31)(23,25,32)(27,36,30)(28,34,39)(29,33,40)(35,43,38)(37,41,45)(42,46,44);(21,25,27)(26,33,35)(34,41,42);(20,22,28,23,29,37,30,38,44)(21,26,34,25,33,41,27,35,42)(24,31,39,32,40,45,36,43,46)

Conjugacy classes & character table

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

Relationships

Fitting subgroup of	#28353430, #28353450, #28353451, …
maximal subgroup of	C₁₉×#10624526, C₁₉×#10624530, C₁₉×#10624724, …
maximal normal subgroup of	C₁₉×#10624526, C₁₉×#10624530, C₁₉×#10624724, …
maximal quotient of	C₁₉×#10624583, C₁₉×#10624585, C₁₉×#10624587, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4617, 55);

C19×#6908 #17987294