C₁₉×#13630 #18019589

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×#13630

Subgroups

	subgroup	G/H
center	C₁₆×C₁₉	C₂×D₄
commutator	C₄	C₂²×C₁₆×C₁₉
Frattini, cosocle	C₂×C₁₆	C₂³×C₁₉
socle	C₂×C₁₉	C₂×C₄⋊C₁₆
prime radical	C₂³×C₁₉	M₃₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₁₆×C₁₉ ◁ C₂²×C₁₆×C₁₉ ◁ G

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

normal subgroups only

This group has 198 conjugacy classes of subgroups — too many to draw. Only its 154 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)(20,21,24,30,25,31,42,53,26,29,43,51,45,52,68,74,27,32,44,54,46,55,69,75,23,39,40,65,41,66,67,81)(22,33,36,57,37,58,62,78,38,48,63,71,64,72,80,82,34,56,59,76,60,77,79,83,35,28,47,49,61,50,70,73);(20,22,23,35,27,34,26,38)(21,28,29,33,32,48,39,56)(24,36,40,47,44,59,43,63)(25,37,41,61,46,60,45,64)(30,49,51,57,54,71,65,76)(31,50,52,58,55,72,66,77)(42,62,67,70,69,79,68,80)(53,73,74,78,75,82,81,83);(22,34)(28,48)(33,56)(35,38)(36,59)(37,60)(47,63)(49,71)(50,72)(57,76)(58,77)(61,64)(62,79)(70,80)(73,82)(78,83)

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, 6618);