C₁₉×#13447 #18019406

order	4864
nilpotency class	4
isoclinism	isoclinic class of #13312
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₉×#13447

Subgroups

	subgroup	G/H
center	C₄×C₁₉	#469
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₁₉
socle	C₂×C₁₉	#2054
prime radical	C₁₉×#3414	C₂
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ C₁₉×#405 ◁ G

386 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 106 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)(22,35)(23,41)(24,48)(25,51)(26,31)(27,53)(28,34)(29,37)(30,44)(32,50)(33,49)(36,55)(38,65)(39,57)(40,64)(42,66)(43,74)(45,63)(46,77)(47,71)(52,59)(54,56)(58,70)(60,72)(61,75)(62,76)(67,79)(68,82)(69,81)(73,83)(78,80);(20,22)(21,29)(23,42)(24,38)(25,52)(26,37)(27,54)(28,40)(30,60)(31,56)(32,64)(33,65)(34,59)(35,48)(36,45)(39,49)(41,55)(43,68)(44,69)(46,67)(47,73)(50,70)(51,57)(53,58)(61,82)(62,83)(63,79)(66,74)(71,81)(72,75)(76,78)(77,80);(20,23,24,43,49,75,25,44,28,47,50,76,27,46,26,45)(21,30,31,61,53,74,32,41,34,63,51,77,33,62,48,71)(22,36,37,67,54,78,70,73,40,69,52,72,39,68,38,42)(29,55,35,66,65,82,57,60,59,81,64,83,58,80,56,79)

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, 6435);