C₁₉×#7421 #18013380

order	4864
nilpotency class	5
isoclinism	isoclinic class of #7418
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₁₉ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₉×#7421

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	#357
commutator	C₂×C₁₆	C₂×C₄×C₁₉
Frattini, cosocle	C₂²×C₁₆	C₂²×C₁₉
prime radical	C₂³×C₁₉	SD₃₂
LCS	G ▷ C₂×C₁₆ ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ C₂²×C₈×C₁₉ ◁ C₂²×C₁₆×C₁₉ ◁ G

140 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 140 conjugacy classes of subgroups — too many to draw. Only its 50 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) = 2432

A minimal faithful permutation representation — 2 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)(22,26,27,24)(23,25)(28,29,32,38,35,42,58,41)(30,43,45,77,48,80,56,79)(31,49,52,86,55,72,91,87)(33,59,57,39,34,61,51,40)(36,63,64,44,68,81,67,83)(37,69,71,54,74,89,73,53)(46,84,60,78,47,85,62,70)(50,75,88,65,82,76,90,66);(20,22)(21,24)(23,27)(25,26)(28,30,35,48)(29,36,42,68)(31,50,55,82)(32,56,58,45)(33,60,34,62)(37,70,74,78)(38,67,41,64)(39,75,40,76)(43,49,80,72)(44,53,83,54)(46,51,47,57)(52,90,91,88)(59,65,61,66)(63,69,81,89)(71,85,73,84)(77,87,79,86)

Conjugacy classes & character table

931 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 409);