C₁₉×#10133 #18016092

order	4864
nilpotency class	3
isoclinism	isoclinic class of #10128
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₉×#10133

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	#392
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
prime radical	C₂²×D₄×C₁₉	D₄
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

536 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 536 conjugacy classes of subgroups — too many to draw. Only its 102 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) = 59
transitive degree	μ_t(G) = 1216

A minimal faithful permutation representation — 3 generators on 59 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(21,24)(22,26)(25,27)(28,29,34,39)(30,40,43,51)(31,36,47,54)(32,38,33,37)(35,44,50,42)(41,56,57,52)(45,59,58,49)(46,55,48,53);(22,26)(24,27)(28,30)(29,35)(31,45)(32,44)(33,42)(34,43)(36,52)(37,51)(38,40)(39,50)(41,46)(47,58)(48,57)(49,53)(54,56)(55,59);(20,21)(22,27)(23,25)(24,26)(28,31,34,47)(29,36,39,54)(30,41,43,57)(32,46,33,48)(35,49,50,59)(37,53,38,55)(40,52,51,56)(42,45,44,58)

Conjugacy classes & character table

589 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 3121);