C₁₉×#13608 #18019567

order	4864
nilpotency class	5
isoclinism	isoclinic class of #13605
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₉×#13608

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₉	#2127
commutator	C₄²	C₂²×C₄×C₁₉
Frattini, cosocle	#124	C₂³×C₁₉
prime radical	C₂×#41×C₁₉	D₄
LCS	G ▷ C₄² ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂²×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ C₁₉×#536 ◁ G

308 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 308 conjugacy classes of subgroups — too many to draw. Only its 86 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)(22,32,35,59)(23,28)(24,40,42,74)(25,44,46,30)(26,31)(27,34,48,65)(29,43)(33,58,62,80)(36,55,45,60)(37,68,41,73)(38,70,72,53)(39,54)(47,64,78,83)(49,66,50,67)(51,61,79,82)(52,69)(56,75)(57,76)(63,77,71,81);(20,22,26,36)(21,27,31,50)(23,33,39,63)(24,34,42,67)(25,45,46,35)(28,51,54,47)(29,55,57,32)(30,48,44,49)(37,61,41,64)(38,71,72,62)(40,60,74,59)(43,65,76,66)(52,77,56,58)(53,79,70,78)(68,81,73,80)(69,82,75,83);(20,23,26,39)(21,28,31,54)(22,33,36,63)(24,41,42,37)(25,38,46,72)(27,47,50,51)(29,56,57,52)(30,53,44,70)(32,58,55,77)(34,64,67,61)(35,62,45,71)(40,73,74,68)(43,75,76,69)(48,78,49,79)(59,80,60,81)(65,83,66,82)

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, 6596);