C₁₉×#6903 #17987289

order	4617
nilpotency class	2
isoclinism	isoclinic class of H(3,𝔽₃)
automorphism	?
homology	Abelianization (H₁) = C₃²×C₉×C₁₉ · Schur multiplier (H₂) = C₃²

Aliases

direct product

C₁₉×#6903

Subgroups

	subgroup	G/H
center	C₁₉×C₂₇	C₃²
commutator	C₃	C₃²×C₉×C₁₉
Frattini, cosocle	C₉	C₃³×C₁₉
socle	C₃×C₁₉	C₃²×C₉
prime radical	C₁₉×H(3,𝔽₃)	C₉
LCS	G ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₁₉×C₂₇ ◁ G

110 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 100
transitive degree	μ_t(G) = 1539

A minimal faithful permutation representation — 3 generators on 100 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,25,23,27,37,33,43,58,24,28,38,34,44,59,52,67,81,35,45,60,53,68,82,74,88,96)(22,26,36,31,41,56,50,65,79,32,42,57,51,66,80,73,87,95,30,40,55,49,64,78,72,86,94)(29,39,54,47,62,76,70,84,92,46,61,75,69,83,91,89,97,99,48,63,77,71,85,93,90,98,100);(20,22,29)(21,26,39)(23,31,47)(24,32,46)(25,36,54)(27,41,62)(28,42,61)(30,48,35)(33,50,70)(34,51,69)(37,56,76)(38,57,75)(40,63,45)(43,65,84)(44,66,83)(49,71,53)(52,73,89)(55,77,60)(58,79,92)(59,80,91)(64,85,68)(67,87,97)(72,90,74)(78,93,82)(81,95,99)(86,98,88)(94,100,96);(22,30,32)(26,40,42)(29,46,48)(31,49,51)(36,55,57)(39,61,63)(41,64,66)(47,69,71)(50,72,73)(54,75,77)(56,78,80)(62,83,85)(65,86,87)(70,89,90)(76,91,93)(79,94,95)(84,97,98)(92,99,100)

Conjugacy classes & character table

1881 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	#28353356, #28353359, #28354839, …
maximal subgroup of	C₁₉×#10624503, C₁₉×#10624504, C₁₉×#10624724, …
maximal normal subgroup of	C₁₉×#10624503, C₁₉×#10624504, C₁₉×#10624724, …
maximal quotient of	C₁₉×#10624681, C₁₉×#10624684, C₁₉×#10624707, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4617, 50);

C19×#6903 #17987289