C₁₉×#11914 #18017873

order	4864
nilpotency class	4
isoclinism	isoclinic class of #11912
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₉×#11914

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₉	#1530
commutator	C₄²	C₂²×C₄×C₁₉
Frattini, cosocle	#97	C₂³×C₁₉
prime radical	C₂³×C₁₉	#100
LCS	G ▷ C₄² ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂×C₄×C₁₉ ◁ C₁₉×#405 ◁ G

272 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 94 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)(20,21,24,30,25,31,45,61,26,32,44,62,47,29,56,58)(22,33,35,64,36,27,48,50,37,51,69,59,46,52,42,75)(23,38,40,70,41,55,73,60,39,57,43,77,71,28,53,54)(34,49,66,79,67,78,76,82,65,80,68,81,74,63,72,83);(20,22,26,37)(21,27,32,52)(23,34,39,65)(24,42,44,48)(25,46,47,36)(28,49,55,80)(29,51,31,33)(30,59,62,64)(35,45,69,56)(38,63,57,78)(40,72,43,76)(41,74,71,67)(50,58,75,61)(53,66,73,68)(54,82,60,83)(70,79,77,81);(20,23,26,39)(21,28)(22,34,37,65)(24,43,44,40)(25,41,47,71)(27,49)(29,57)(30,60)(31,38)(32,55)(33,63)(35,68,69,66)(36,67,46,74)(42,76,48,72)(45,53,56,73)(50,81)(51,78)(52,80)(54,62)(58,70)(59,83)(61,77)(64,82)(75,79)

Conjugacy classes & character table

646 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 4902);