C₁₉×#12463 #18018422

order	4864
nilpotency class	4
isoclinism	isoclinic class of #12463
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₉×#12463

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₉	#1675
commutator, Frattini, cosocle	C₄×C₈	C₂³×C₁₉
prime radical	C₁₉×#135	D₄
LCS	G ▷ C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂×C₄×C₁₉ ◁ C₄×C₈×C₁₉ ◁ G

172 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 172 conjugacy classes of subgroups — too many to draw. Only its 74 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)(20,21,27,33)(22,34,39,66)(23,40)(24,45,47,31)(25,30,49,61)(26,50,46,32)(28,51,55,36)(29,56)(35,67)(37,64,74,54)(38,53,72,65)(41,60)(42,76)(43,62)(44,57)(48,58)(52,69)(59,77)(63,78)(68,75)(70,80)(71,79)(73,82)(81,83);(20,22,25,37,26,38,47,51,27,39,49,74,46,72,24,36)(21,28,45,65,32,54,61,66,33,55,31,53,50,64,30,34)(23,35,48,73,42,69,56,78,44,71,77,83,43,70,41,68)(29,52,76,82,58,67,40,75,60,80,62,81,59,79,57,63);(20,23)(21,29)(22,35)(24,41)(25,48)(26,42)(27,44)(28,52)(30,57)(31,62)(32,58)(33,60)(34,63)(36,68)(37,73)(38,69)(39,71)(40,61)(43,46)(45,76)(47,56)(49,77)(50,59)(51,78)(53,81)(54,67)(55,80)(64,79)(65,82)(66,75)(70,72)(74,83)

Conjugacy classes & character table

703 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 5451);