C₁₉×#13441 #18019400

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

Aliases

direct product

C₁₉×#13441

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	#466
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₁₉
prime radical	C₂³×C₁₉	#135
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ C₁₉×#405 ◁ G

378 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 378 conjugacy classes of subgroups — too many to draw. Only its 110 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)(24,25,30,35)(26,36,40,68)(27,41,46,59)(28,47,51,66)(29,52,49,34)(31,54,57,38)(32,43,61,44)(33,62,64,50)(37,69,72,85)(39,73,53,63)(42,67,70,58)(45,81,78,75)(48,65,83,56)(55,76,84,71)(60,80,74,79)(77,86,82,87);(24,26,30,40)(25,31,35,57)(27,42,46,70)(28,48,51,83)(29,53,49,39)(32,58,61,67)(33,63,64,73)(34,65,52,56)(36,66,68,47)(37,43,72,44)(38,62,54,50)(41,55,59,84)(45,82,78,77)(60,87,74,86)(69,75,85,81)(71,80,76,79);(21,23)(24,27,28,43,49,78,62,80,30,46,51,44,29,45,50,79)(25,32,33,59,52,74,66,75,35,61,64,41,34,60,47,81)(26,37,38,70,53,76,83,77,40,72,54,42,39,71,48,82)(31,55,36,67,65,85,73,86,57,84,68,58,56,69,63,87)

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, 6429);