C₁₉×#13435 #18019394

order	4864
nilpotency class	4
isoclinism	isoclinic class of #13432
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₉×#13435

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

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

normal subgroups only

This group has 408 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)(22,32,36,54)(23,37,41,66)(24,42,45,29)(25,46,47,30)(27,43,50,34)(28,51,53,40)(33,58,38,67)(35,62,63,57)(39,70,72,65)(44,55,76,74)(48,78,80,83)(49,61,77,75)(52,71,73,81)(56,69,82,60)(59,79,68,64);(20,22,26,36)(21,27,31,50)(23,38,41,33)(24,43,45,34)(25,35,47,63)(28,48,53,80)(29,54,42,32)(30,49,46,77)(37,64,66,79)(39,59,72,68)(40,60,51,69)(44,75,76,61)(52,82,73,56)(55,62,74,57)(58,70,67,65)(71,78,81,83);(20,23,24,39,26,41,45,72)(21,28,29,52,31,53,42,73)(22,33,34,59,36,38,43,68)(25,40,44,71,47,51,76,81)(27,48,32,56,50,80,54,82)(30,37,55,65,46,66,74,70)(35,60,61,83,63,69,75,78)(49,79,57,58,77,64,62,67)

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, 6423);