C₁₉×#13724 #18019683

order	4864
nilpotency class	5
isoclinism	isoclinic class of #13697
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₄

Aliases

direct product

C₁₉×#13724

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂²×C₁₉	C₂×D₁₆
commutator, Frattini, cosocle	C₂×C₁₆	C₂³×C₁₉
LCS	G ▷ C₂×C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₄²×C₁₉ ◁ C₄×C₈×C₁₉ ◁ C₄×C₁₆×C₁₉ ◁ G

174 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 174 conjugacy classes of subgroups — too many to draw. Only its 78 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) = 91
transitive degree	μ_t(G) = 4864

A minimal faithful permutation representation — 3 generators on 91 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21)(22,25)(23,24)(26,27)(28,29,36,43)(30,38,48,68)(31,37,51,65)(32,40,54,61)(33,39,44,70)(34,57,59,86)(35,60,58,42)(41,73,74,52)(45,66,75,90)(46,79,81,91)(47,82,80,67)(49,62,83,87)(50,84,77,64)(53,85,55,72)(56,71,76,69)(63,88,89,78);(21,24)(25,27)(28,30,44,75,34,46,53,50,58,80,56,78,73,83,32,31,36,48,33,45,59,81,55,77,35,47,76,88,52,49,54,51)(29,37,61,87,41,63,69,67,60,84,72,79,86,90,39,38,43,65,40,62,74,89,71,82,42,64,85,91,57,66,70,68);(20,22,23,26)(21,25,24,27)(28,31,32,49,52,78,56,47,35,50,53,81,59,75,44,48,36,51,54,83,73,88,76,80,58,77,55,46,34,45,33,30)(29,38,39,66,57,79,72,64,42,67,69,89,74,87,61,65,43,68,70,90,86,91,85,84,60,82,71,63,41,62,40,37)

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, 6712);