C₁₉×#13648 #18019607

order	4864
nilpotency class	3
isoclinism	isoclinic class of AGL(1,ℤ/8)
automorphism	?
homology	Abelianization (H₁) = C₂²×C₁₆×C₁₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₉×#13648

Subgroups

	subgroup	G/H
center	C₁₆×C₁₉	C₂×D₄
commutator	C₄	C₂²×C₁₆×C₁₉
Frattini, cosocle	C₂×C₁₆	C₂³×C₁₉
socle	C₂×C₁₉	D₄×C₁₆
prime radical	C₁₉×#135	C₈
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₁₆×C₁₉ ◁ C₂×C₁₉×C₃₂ ◁ G

184 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 118 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)(20,21,25,32,26,33,50,65,27,31,51,63,53,64,56,81,28,34,52,66,54,36,68,70,24,46,48,77,49,69,74,80)(22,35,38,67,39,44,72,76,37,29,55,57,71,45,30,60,40,58,62,82,73,42,61,75,47,59,78,83,79,23,41,43);(20,22)(21,29)(23,36)(24,47)(25,38)(26,39)(27,37)(28,40)(30,56)(31,58)(32,57)(33,45)(34,59)(35,46)(41,74)(42,64)(43,70)(44,69)(48,78)(49,79)(50,72)(51,55)(52,62)(53,71)(54,73)(60,65)(61,68)(63,82)(66,83)(67,77)(75,81)(76,80);(20,23,25,43,26,35,50,67,27,44,51,76,53,29,56,57,28,45,52,60,54,58,68,82,24,42,48,75,49,59,74,83)(21,30,32,40,33,62,65,73,31,61,63,47,64,78,81,79,34,41,66,22,36,38,70,39,46,72,77,37,69,55,80,71)

Conjugacy classes & character table

1672 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 6636);