C₁₉×#13362 #18019321

order	4864
nilpotency class	4
isoclinism	isoclinic class of #13360
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₉×#13362

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₉	#2021
commutator, Frattini, cosocle	C₂×#41	C₂³×C₁₉
prime radical	C₁₉×#585	C₂²
LCS	G ▷ C₂×#41 ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂×C₄×C₁₉ ◁ C₂×#41×C₁₉ ◁ G

670 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 670 conjugacy classes of subgroups — too many to draw. Only its 94 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)(20,21,27,32)(22,33,37,59)(23,38,43,63)(24,44,48,30)(25,49,26,31)(28,45,55,35)(29,42,58,41)(34,66,68,82)(36,71,50,65)(39,64,72,83)(40,75,46,73)(47,61,51,62)(52,76,81,74)(53,69,54,70)(56,67,80,79)(57,77,60,78);(20,22)(21,28)(23,39)(24,45)(25,36)(26,50)(27,37)(29,56)(30,59)(31,53)(32,55)(33,44)(34,42)(35,48)(38,52)(40,76)(41,68)(43,72)(46,74)(47,70)(49,54)(51,69)(57,66)(58,80)(60,82)(61,71)(62,65)(63,81)(64,75)(67,77)(73,83)(78,79);(20,23,27,43)(21,29,32,58)(22,34,37,68)(24,46,48,40)(25,42,26,41)(28,52,55,81)(30,60,44,57)(31,63,49,38)(33,64,59,83)(35,67,45,79)(36,72,50,39)(47,77,51,78)(53,56,54,80)(61,73,62,75)(65,82,71,66)(69,76,70,74)

Conjugacy classes & character table

532 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 6350);