C₁₉×#12466 #18018425

order	4864
nilpotency class	4
isoclinism	isoclinic class of #12465
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₉×#12466

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₉	#1677
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

186 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 186 conjugacy classes of subgroups — too many to draw. Only its 70 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)(20,21,28,35)(22,36,43,68)(23,44,48,60)(24,32,49,54)(25,31,37,63)(26,34,27,33)(29,53,59,39)(30,45,62,46)(38,70,73,82)(40,57,50,58)(41,56,42,64)(47,77,52,65)(51,66,69,61)(55,76,80,72)(67,74,79,71)(75,81,78,83);(20,22,37,40,26,41,24,39,28,43,25,50,27,42,49,53)(21,29,54,56,33,57,31,36,35,59,32,64,34,58,63,68)(23,38,69,75,47,72,46,74,48,73,51,78,52,76,45,71)(30,55,77,81,61,70,44,67,62,80,65,83,66,82,60,79);(20,23)(21,30)(22,38)(24,46)(25,51)(26,47)(27,52)(28,48)(29,55)(31,44)(32,65)(33,61)(34,66)(35,62)(36,67)(37,69)(39,74)(40,75)(41,72)(42,76)(43,73)(45,49)(50,78)(53,71)(54,77)(56,81)(57,70)(58,82)(59,80)(60,63)(64,83)(68,79)

Conjugacy classes & character table

589 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 5454);