C₁₉×#13615 #18019574

order	4864
nilpotency class	5
isoclinism	isoclinic class of D₃₂
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₉×#13615

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₉	D₁₆
commutator	C₁₆	C₂²×C₄×C₁₉
Frattini, cosocle	C₂×C₁₆	C₂³×C₁₉
socle	C₂²×C₁₉	C₂×D₁₆
prime radical	C₂×C₁₉×#508	C₂
LCS	G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ C₂²×C₈×C₁₉ ◁ C₂²×C₁₆×C₁₉ ◁ G

298 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 298 conjugacy classes of subgroups — too many to draw. Only its 126 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) = 87
transitive degree	μ_t(G) = 2432

A minimal faithful permutation representation — 3 generators on 87 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,22,23)(24,25)(26,37)(27,32)(28,46)(29,50)(30,36)(31,39)(33,48)(34,44)(35,45)(38,64)(40,70)(41,72)(42,65)(43,73)(47,61)(49,79)(51,58)(52,57)(53,66)(54,80)(55,69)(56,75)(59,85)(60,82)(62,77)(63,68)(67,84)(71,86)(74,83)(76,78)(81,87);(24,26)(25,31)(27,38)(28,47)(29,51)(30,42)(32,53)(33,58)(34,61)(35,63)(36,55)(37,46)(39,48)(40,44)(41,45)(43,74)(49,81)(50,54)(52,67)(56,70)(57,83)(59,86)(60,84)(62,87)(64,73)(65,79)(66,75)(68,85)(69,82)(71,77)(72,78)(76,80);(24,27,30,45)(25,32,36,35)(26,38,42,41)(28,43,49,76)(29,44,52,77)(31,53,55,63)(33,56,60,59)(34,57,62,50)(37,64,65,72)(39,66,69,68)(40,67,71,51)(46,73,79,78)(47,74,81,80)(48,75,82,85)(54,61,83,87)(58,70,84,86)

Conjugacy classes & character table

1444 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 6603);