C₁₉×#12423 #18018382

order	4864
nilpotency class	4
isoclinism	isoclinic class of #12416
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₉×#12423

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂²×C₁₉	#459
commutator, Frattini, cosocle	C₄×C₈	C₂³×C₁₉
LCS	G ▷ C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₄²×C₁₉ ◁ C₈²×C₁₉ ◁ G

218 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 82 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) = 4864

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)(28,29,31,34)(30,38,39,56)(32,44,42,57)(33,47,43,37)(35,51,49,40)(36,53,50,46)(41,58,48,54)(45,55,59,52);(20,21,22,24,23,25,26,27)(29,34)(35,49)(36,50)(37,47)(38,56)(44,57)(52,55)(54,58);(28,30,31,39)(29,35,34,49)(32,45,42,59)(33,48,43,41)(36,54,50,58)(37,55,47,52)(38,57,56,44)(40,53,51,46)

Conjugacy classes & character table

817 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 5411);