C₁₉×#13431 #18019390

order	4864
nilpotency class	4
isoclinism	isoclinic class of #13429
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₉×#13431

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₉	#2044
commutator, Frattini, cosocle	C₂×#41	C₂³×C₁₉
prime radical	C₂×#41×C₁₉	C₂³
LCS	G ▷ C₂×#41 ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂×C₄×C₁₉ ◁ C₂×#41×C₁₉ ◁ G

402 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 86 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)(20,21,26,31)(22,32,36,53)(23,37,41,55)(24,42,45,29)(25,30,47,56)(27,43,50,34)(28,46,52,40)(33,59,38,68)(35,58,64,82)(39,70,72,67)(44,66,73,54)(48,77,79,83)(49,75,80,62)(51,71,74,76)(57,63,81,61)(60,78,69,65);(20,22,26,36)(21,27,31,50)(23,38,41,33)(24,43,45,34)(25,35,47,64)(28,48,52,79)(29,53,42,32)(30,49,56,80)(37,65,55,78)(39,60,72,69)(40,61,46,63)(44,75,73,62)(51,81,74,57)(54,82,66,58)(59,70,68,67)(71,77,76,83);(20,23,24,39,26,41,45,72)(21,28,29,51,31,52,42,74)(22,33,34,60,36,38,43,69)(25,46,44,76,47,40,73,71)(27,48,32,57,50,79,53,81)(30,55,54,70,56,37,66,67)(35,63,62,77,64,61,75,83)(49,65,58,68,80,78,82,59)

Conjugacy classes & character table

532 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 6419);