C₁₉×#13709 #18019668

order	4864
nilpotency class	5
isoclinism	isoclinic class of #13709
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₉×#13709

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₉	#2226
commutator, Frattini, cosocle	C₂×C₁₆	C₂³×C₁₉
prime radical	C₁₉×#508	C₂²
LCS	G ▷ C₂×C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂×C₄×C₁₉ ◁ C₄×C₈×C₁₉ ◁ C₄×C₁₆×C₁₉ ◁ G

154 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 154 conjugacy classes of subgroups — too many to draw. Only its 70 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 — 3 generators on 83 points:

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

Conjugacy classes & character table

703 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 6697);