C₁₉×#7391 #18013350

order	4864
nilpotency class	5
isoclinism	isoclinic class of #7389
automorphism	?
homology	Abelianization (H₁) = C₂×C₈×C₁₉ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₉×#7391

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₉	#1333
commutator	C₁₆	C₂×C₈×C₁₉
Frattini, cosocle	#346	C₂²×C₁₉
prime radical	C₂²×C₁₉	#361
LCS	G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂×C₄×C₁₉ ◁ C₄×C₈×C₁₉ ◁ C₁₉×#346 ◁ G

116 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 116 conjugacy classes of subgroups — too many to draw. Only its 50 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 — 2 generators on 83 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,24,30,26,32,48,60,27,34,25,49,47,33,51,31)(22,35,37,59,38,68,45,67,39,70,72,82,52,69,50,81)(23,40,42,64,43,65,79,63,44,77,46,29,58,61,71,62)(28,41,53,36,55,73,66,75,57,78,83,76,56,74,54,80);(20,22,27,39)(21,28,34,57)(23,41,44,78)(24,45,25,50)(26,52,47,38)(29,59,64,82)(30,54,49,66)(31,53,60,83)(32,56,33,55)(35,65,70,61)(36,71,76,79)(37,51,72,48)(40,69,77,68)(42,75,46,80)(43,74,58,73)(62,81,63,67)

Conjugacy classes & character table

646 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 379);