C₁₉×#12302 #18018261

order	4864
nilpotency class	4
isoclinism	isoclinic class of #12301
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₉×#12302

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₉	#1613
commutator, Frattini, cosocle	C₂×M₁₆	C₂³×C₁₉
prime radical	C₂×#41×C₁₉	D₄
LCS	G ▷ C₂×M₁₆ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂×C₄×C₁₉ ◁ C₂×M₁₆×C₁₉ ◁ G

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

normal subgroups only

This group has 310 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)(20,21,26,31,27,33,25,32)(22,34,38,55,39,63,37,62)(23,40,42,29,43,58,48,54)(24,44,46,30,47,59,49,57)(28,45,60,36,52,68,51,69)(35,64,66,61,67,82,70,79)(41,56,75,72,76,53,74,77)(50,78,71,73,81,65,80,83);(20,22,27,39)(21,28,33,52)(23,35,43,67)(24,45,47,68)(25,38,26,37)(29,50,54,81)(30,55,57,62)(31,51,32,60)(34,44,63,59)(36,46,69,49)(40,71,58,80)(41,73,76,83)(42,70,48,66)(53,64,56,82)(61,77,79,72)(65,75,78,74);(20,23)(21,29)(22,35)(24,41)(25,48)(26,42)(27,43)(28,50)(30,56)(31,58)(32,40)(33,54)(34,61)(36,65)(37,70)(38,66)(39,67)(44,77)(45,73)(46,75)(47,76)(49,74)(51,80)(52,81)(53,57)(55,82)(59,72)(60,71)(62,64)(63,79)(68,83)(69,78)

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, 5290);