C₁₉×#12118 #18018077

order	4864
nilpotency class	4
isoclinism	isoclinic class of #12117
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₉×#12118

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₉	#1595
commutator, Frattini, cosocle	C₂×M₁₆	C₂³×C₁₉
prime radical	C₁₉×#2017	C₂
LCS	G ▷ C₂×M₁₆ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂×C₄×C₁₉ ◁ C₂×M₁₆×C₁₉ ◁ G

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

normal subgroups only

This group has 392 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)(22,34)(23,39)(24,43)(25,32)(26,31)(27,33)(28,36)(29,41)(30,46)(35,63)(37,71)(38,62)(40,74)(42,59)(44,52)(45,55)(47,60)(48,56)(49,58)(50,57)(51,78)(53,69)(54,70)(61,65)(64,72)(66,83)(67,81)(68,79)(73,77)(75,80)(76,82);(20,22,27,38)(21,28,33,54)(23,35,42,67)(24,44,47,69)(25,37,26,50)(29,51,56,80)(30,57,58,71)(31,53,32,52)(34,60,62,43)(36,49,70,46)(39,72,59,79)(40,75,45,78)(41,65,48,66)(55,81,74,63)(61,82,83,73)(64,76,68,77);(20,23)(21,29)(22,35)(24,45)(25,48)(26,41)(27,42)(28,51)(30,55)(31,59)(32,39)(33,56)(34,61)(36,68)(37,66)(38,67)(40,47)(43,73)(44,78)(46,76)(49,77)(50,65)(52,72)(53,79)(54,80)(57,81)(58,74)(60,82)(62,83)(63,71)(64,70)(69,75)

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, 5106);