C₁₉×#32949 #18038908

order	4864
nilpotency class	3
isoclinism	isoclinic class of #32947
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₉ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product

C₁₉×#32949

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₉	#2847
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₁₉×#585	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ G

1278 conjugacy classes of subgroups; only the 290 normal subgroups are shown.

normal subgroups only

This group has 1278 conjugacy classes of subgroups — too many to draw. Only its 290 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 — 4 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)(22,32,37,55)(23,28,40,50)(24,29,42,52)(25,43,33,30)(27,44,47,36)(34,53,60,75)(35,54,62,76)(38,63,65,48)(39,66,56,49)(41,67,57,51)(45,68,71,59)(46,69,72,61)(58,78,80,74)(64,73,77,82)(70,79,81,83);(20,22,33,44,26,37,25,36)(21,27,43,55,31,47,30,32)(23,34,56,68,40,60,39,59)(24,35,57,69,42,62,41,61)(28,45,66,75,50,71,49,53)(29,46,67,76,52,72,51,54)(38,58,77,83,65,80,64,79)(48,70,82,78,63,81,73,74);(20,23)(21,28)(22,34)(24,38)(25,39)(26,40)(27,45)(29,48)(30,49)(31,50)(32,53)(33,56)(35,58)(36,59)(37,60)(41,64)(42,65)(43,66)(44,68)(46,70)(47,71)(51,73)(52,63)(54,74)(55,75)(57,77)(61,79)(62,80)(67,82)(69,83)(72,81)(76,78);(20,24)(21,29)(22,35)(23,38)(25,41)(26,42)(27,46)(28,48)(30,51)(31,52)(32,54)(33,57)(34,58)(36,61)(37,62)(39,64)(40,65)(43,67)(44,69)(45,70)(47,72)(49,73)(50,63)(53,74)(55,76)(56,77)(59,79)(60,80)(66,82)(68,83)(71,81)(75,78)

Conjugacy classes & character table

874 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 25937);