C₁₉×#7229 #18013188

order	4864
nilpotency class	3
isoclinism	isoclinic class of #7225
automorphism	?
homology	Abelianization (H₁) = C₄²×C₁₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₉×#7229

Subgroups

	subgroup	G/H
center	C₄×C₁₉	H(3,ℤ/4)
commutator	C₂×C₈	C₄²×C₁₉
Frattini, cosocle	C₂×#131	C₂²×C₁₉
socle	C₂×C₁₉	#1289
prime radical	C₂×#41×C₁₉	D₄
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₁
UCS	C₁ ◁ C₄×C₁₉ ◁ C₂×C₈×C₁₉ ◁ G

244 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 244 conjugacy classes of subgroups — too many to draw. Only its 86 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 — 2 generators on 83 points:

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

Conjugacy classes & character table

760 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 217);