C₁₉×#6909 #17987295

order	4617
nilpotency class	3
isoclinism	isoclinic class of #6909
automorphism	?
homology	Abelianization (H₁) = C₃³×C₁₉ · Schur multiplier (H₂) = C₃³

Aliases

direct product

C₁₉×#6909

Subgroups

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

148 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)(22,28,33)(23,27,34)(25,35,31)(26,38,32)(29,40,43)(30,37,44)(36,46,42)(39,45,41);(20,22,29)(21,25,36)(23,31,41)(24,33,43)(26,28,39)(27,37,40)(30,42,32)(34,35,45)(38,44,46);(22,30,31)(25,28,37)(29,41,42)(33,44,35)(36,40,39)(43,45,46)

Conjugacy classes & character table

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

Relationships

Fitting subgroup of	#28354978, #28354983, #28354985, …
maximal subgroup of	C₁₉×UT(4,𝔽₃), C₁₉×#10624748, C₁₉×#10624749, …
maximal normal subgroup of	C₁₉×UT(4,𝔽₃), C₁₉×#10624748, C₁₉×#10624749, …
maximal quotient of	C₁₉×#10624590, C₁₉×#10624591, C₁₉×#10624594, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4617, 56);

C19×#6909 #17987295