C₁₉×#9336 #18015295

order	4864
nilpotency class	3
isoclinism	isoclinic class of #9331
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₉×#9336

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	#386
commutator	C₂²×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
prime radical	C₂³×C₁₉	C₄×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

360 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 114 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) = 83
transitive degree	μ_t(G) = 2432

A minimal faithful permutation representation — 3 generators on 83 points:

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

Conjugacy classes & character table

646 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 2324);