C₁₉×#12026 #18017985

order	4864
nilpotency class	4
isoclinism	isoclinic class of #12026
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₉×#12026

Subgroups

	subgroup	G/H
center	C₄×C₁₉	#427
commutator	C₂×C₈	C₂²×C₄×C₁₉
Frattini, cosocle	C₄×C₈	C₂³×C₁₉
socle	C₂×C₁₉	#1568
prime radical	C₂³×C₁₉	#108
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₉ ◁ C₁₉×#97 ◁ C₁₉×#405 ◁ G

180 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 180 conjugacy classes of subgroups — too many to draw. Only its 106 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)(20,21,25,32,27,33,50,62,28,34,49,31,26,53,24,48)(22,35,38,55,40,64,37,56,41,60,51,77,39,73,71,29)(23,42,44,75,46,59,43,61,47,76,52,78,45,30,57,58)(36,65,67,54,69,79,81,74,70,83,72,80,68,63,66,82);(20,22,24,37,26,39,49,38,28,41,50,71,27,40,25,51)(21,29,31,35,33,55,48,64,34,56,32,60,53,77,62,73)(23,36,43,66,45,68,44,72,47,70,57,81,46,69,52,67)(30,54,58,63,42,74,75,65,59,80,61,79,76,82,78,83);(20,23,26,45,28,47,27,46)(21,30,33,42,34,59,53,76)(22,36,39,68,41,70,40,69)(24,43,49,44,50,57,25,52)(29,54,55,74,56,80,77,82)(31,58,48,75,32,61,62,78)(35,63,64,65,60,79,73,83)(37,66,38,72,71,81,51,67)

Conjugacy classes & character table

988 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 5014);