C₁₉×#12893 #18018852

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

Aliases

direct product

C₁₉×#12893

Subgroups

	subgroup	G/H
center	C₄×C₁₉	#427
commutator	C₂×C₈	C₂²×C₄×C₁₉
Frattini, cosocle	C₂²×C₈	C₂³×C₁₉
socle	C₂×C₁₉	#1835
prime radical	C₂³×C₁₉	#135
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₉ ◁ C₁₉×#117 ◁ C₁₉×#405 ◁ G

234 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 122 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)(22,34)(23,41,44,72)(24,46)(25,30)(26,49)(27,33)(28,37)(29,43,55,75)(31,35)(32,47)(36,64,67,50)(38,59)(39,51)(40,61)(42,73,63,56)(45,76,74,54)(48,57)(52,70)(53,62)(58,66,79,83)(60,69)(65,71,81,80)(68,77,82,78);(20,22,35,62,47,69,25,38,27,40,24,37,26,39,48,70)(21,28,30,34,49,59,31,51,33,53,57,61,32,52,46,60)(23,36,63,81,74,82,43,66,44,67,42,65,45,68,75,83)(29,50,54,58,73,78,41,71,55,64,76,79,56,77,72,80);(20,23,24,42,47,74,48,75,27,44,35,63,26,45,25,43)(21,29,30,54,49,73,31,41,33,55,57,76,32,56,46,72)(22,36,37,65,69,82,70,83,40,67,62,81,39,68,38,66)(28,50,34,58,59,78,51,71,53,64,61,79,52,77,60,80)

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, 5881);