C₁₉×#12305 #18018264

order	4864
nilpotency class	4
isoclinism	isoclinic class of #12304
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₉×#12305

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₉	#1616
commutator, Frattini, cosocle	C₂×M₁₆	C₂³×C₁₉
prime radical	C₂³×C₁₉	C₂×SD₁₆
LCS	G ▷ C₂×M₁₆ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂×C₄×C₁₉ ◁ C₂×M₁₆×C₁₉ ◁ G

262 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 70 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) = 1216

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)(20,21,25,45,26,31,47,30)(22,32,36,54,35,59,46,60)(23,37,40,53,39,28,51,67)(24,41,44,29,43,73,74,56)(27,42,57,34,50,64,49,65)(33,58,62,82,63,76,72,79)(38,68,70,55,71,80,78,52)(48,75,81,83,66,69,77,61);(20,22,26,35)(21,27,31,50)(23,33,39,63)(24,42,43,64)(25,46,47,36)(28,48,37,66)(29,54,56,60)(30,57,45,49)(32,41,59,73)(34,44,65,74)(38,69,71,75)(40,72,51,62)(52,79,55,82)(53,81,67,77)(58,68,76,80)(61,70,83,78);(20,23)(21,28,31,37)(22,33)(24,38)(25,40)(26,39)(27,48,50,66)(29,55,56,52)(30,53,45,67)(32,58,59,76)(34,61)(35,63)(36,62)(41,68,73,80)(42,69)(43,71)(44,70)(46,72)(47,51)(49,77,57,81)(54,82,60,79)(64,75)(65,83)(74,78)

Conjugacy classes & character table

475 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 5293);