C₁₉×#13633 #18019592

order	4864
nilpotency class	5
isoclinism	isoclinic class of D₃₂
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₁₉×#13633

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₉	D₁₆
commutator	C₁₆	C₂²×C₄×C₁₉
Frattini, cosocle	C₂×C₁₆	C₂³×C₁₉
socle	C₂²×C₁₉	C₂×D₁₆
prime radical	C₂³×C₁₉	D₁₆
LCS	G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ C₂²×C₈×C₁₉ ◁ C₂²×C₁₆×C₁₉ ◁ G

190 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 190 conjugacy classes of subgroups — too many to draw. Only its 126 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) = 87
transitive degree	μ_t(G) = 2432

A minimal faithful permutation representation — 3 generators on 87 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,22,23)(24,25)(26,37)(27,33)(28,46)(29,50)(30,52)(31,36)(32,40)(34,38)(35,47)(39,59)(41,72)(42,74)(43,62)(44,75)(45,58)(48,78)(49,77)(51,79)(53,67)(54,81)(55,71)(56,64)(57,66)(60,63)(61,69)(65,76)(68,84)(70,80)(73,87)(82,85)(83,86);(24,26,38,63,29,41,44,67,27,39,64,85,45,68,49,71,31,43,66,86,51,73,48,70,30,42,65,81,47,69,28,40)(25,32,46,61,35,54,76,74,52,80,78,87,79,83,57,62,36,55,77,84,58,82,56,59,33,53,75,72,50,60,34,37);(24,27,31,30)(25,33,36,52)(26,39,43,42)(28,44,49,48)(29,45,51,47)(32,53,55,80)(34,56,57,76)(35,50,58,79)(37,59,62,74)(38,64,66,65)(40,67,71,70)(41,68,73,69)(46,75,77,78)(54,60,82,83)(61,72,84,87)(63,85,86,81)

Conjugacy classes & character table

1444 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 6621);