C₁₉×#13078 #18019037

order	4864
nilpotency class	4
isoclinism	isoclinic class of #13077
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₉×#13078

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₉	#1893
commutator	C₂×C₈	C₂²×C₄×C₁₉
Frattini, cosocle	C₂²×C₈	C₂³×C₁₉
prime radical	C₂×#41×C₁₉	D₄
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ C₂×C₁₉×#131 ◁ G

454 conjugacy classes of subgroups; only the 146 normal subgroups are shown.

normal subgroups only

This group has 454 conjugacy classes of subgroups — too many to draw. Only its 146 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)(20,21,25,32,27,31,26,50)(22,33,37,63,36,60,48,64)(23,38,40,59,41,29,49,58)(24,42,45,52,47,74,46,30)(28,51,54,35,56,70,55,43)(34,62,67,82,66,79,68,83)(39,72,73,61,44,75,76,57)(53,78,80,69,71,77,81,65);(20,22,24,43,26,37,46,51,27,36,47,35,25,48,45,70)(21,28,52,33,32,55,74,64,31,56,30,60,50,54,42,63)(23,34,44,65,40,68,76,77,41,66,39,69,49,67,73,78)(29,53,57,62,59,80,75,82,38,71,61,79,58,81,72,83);(20,23)(21,29)(22,34)(24,44)(25,49)(26,40)(27,41)(28,53)(30,61)(31,38)(32,59)(33,62)(35,69)(36,66)(37,68)(39,47)(42,72)(43,65)(45,73)(46,76)(48,67)(50,58)(51,77)(52,57)(54,81)(55,80)(56,71)(60,79)(63,83)(64,82)(70,78)(74,75)

Conjugacy classes & character table

874 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 6066);