C₁₉×#10667 #18016626

order	4864
nilpotency class	3
isoclinism	isoclinic class of #10012
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₉×#10667

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₉	#127
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
socle	C₂²×C₁₉	#399
prime radical	C₁₉×#532	C₂²
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

354 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 354 conjugacy classes of subgroups — too many to draw. Only its 114 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)(20,21,22,25,23,26,27,24)(28,29,32,37,34,38,33,47)(30,39,41,50,42,55,43,35)(31,36,45,52,46,54,48,53)(40,51,44,49,57,56,58,59);(20,21)(22,24)(23,26)(25,27)(28,30,33,41,34,42,32,43)(29,35,47,39,38,50,37,55)(31,44,48,57,46,58,45,40)(36,51,53,49,54,56,52,59);(21,24)(22,27)(25,26)(28,31)(29,36)(30,40)(32,45)(33,48)(34,46)(35,49)(37,52)(38,54)(39,56)(41,44)(42,57)(43,58)(47,53)(50,59)(51,55)

Conjugacy classes & character table

760 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 3655);