C₁₉×#7831 #18013790

order	4864
nilpotency class	3
isoclinism	isoclinic class of #7734
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₄

Aliases

direct product

C₁₉×#7831

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₉	#120
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
LCS	G ▷ C₂×C₄² ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

350 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 98 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)(21,26)(22,27)(23,24)(28,29,33,36)(30,37,39,42)(31,35,32,40)(34,41,43,38)(44,45,48,51)(46,49,53,56)(47,50,54,57)(52,58,59,55);(20,21,25,22)(23,27,24,26)(28,30)(29,34)(31,38)(32,41)(33,39)(35,42)(36,43)(37,40)(44,46)(45,49)(47,52)(48,53)(50,55)(51,56)(54,59)(57,58);(20,22,25,21)(23,27,24,26)(28,31,33,32)(29,35,36,40)(30,38,39,41)(34,42,43,37)(44,47)(45,50)(46,52)(48,54)(49,55)(51,57)(53,59)(56,58)

Conjugacy classes & character table

703 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 819);