C₁₉×#13312 #18019271

order	4864
nilpotency class	4
isoclinism	isoclinic class of #13312
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₉×#13312

Subgroups

	subgroup	G/H
center	C₄×C₁₉	#469
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₁₉
socle	C₂×C₁₉	#1999
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ C₂×C₁₉×#131 ◁ G

520 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 114 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)(23,40)(24,45)(25,32)(26,31)(27,33)(28,36)(29,43)(30,48)(35,64)(37,70)(38,58)(39,63)(41,73)(42,75)(44,56)(46,61)(47,60)(49,59)(50,57)(51,80)(52,68)(53,69)(54,65)(55,78)(62,66)(67,83)(71,74)(72,77)(76,81)(79,82);(20,22)(21,28)(23,41)(24,46)(25,37)(26,38)(27,39)(29,54)(30,58)(31,52)(32,61)(33,53)(34,45)(35,43)(36,48)(40,71)(42,76)(44,66)(47,69)(49,68)(50,67)(51,56)(55,62)(57,81)(59,63)(60,70)(64,72)(65,78)(73,75)(74,77)(79,80)(82,83);(20,23)(21,29)(22,35)(24,42)(25,50)(26,43)(27,44)(28,51)(30,55)(31,56)(32,40)(33,57)(34,62)(36,65)(37,41)(38,66)(39,67)(45,72)(46,74)(47,79)(48,77)(49,78)(52,81)(53,71)(54,61)(58,83)(59,82)(60,75)(63,73)(64,70)(68,80)(69,76)

Conjugacy classes & character table

760 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 6300);