C₁₉×#13315 #18019274

order	4864
nilpotency class	4
isoclinism	isoclinic class of #13313
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₉×#13315

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	#466
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₁₉
prime radical	C₂×#41×C₁₉	D₄
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ C₂×C₁₉×#131 ◁ G

516 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 516 conjugacy classes of subgroups — too many to draw. Only its 118 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

minimal degree	μ(G) = 87
transitive degree	μ_t(G) = 2432

A minimal faithful permutation representation — 3 generators on 87 points:

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

Conjugacy classes & character table

760 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 6303);