C₁₉×#12027 #18017986

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×#12027

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

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, 5015);