C₁₉×#9991 #18015950

order	4864
nilpotency class	3
isoclinism	isoclinic class of #9986
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₉×#9991

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	#392
commutator, Frattini, cosocle	C₂³×C₄	C₂³×C₁₉
prime radical	C₂⁴×C₁₉	#41
LCS	G ▷ C₂³×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

698 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 698 conjugacy classes of subgroups — too many to draw. Only its 106 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)(22,24)(23,25)(26,27)(28,29,34,39)(30,40,44,51)(31,45,49,54)(32,38,33,37)(35,43,52,42)(36,47,55,48)(41,50,57,58)(46,59,56,53);(24,27)(28,30,34,44)(29,35,39,52)(31,46,49,56)(32,43,33,42)(36,53,55,59)(37,51,38,40)(41,48,57,47)(45,58,54,50);(20,22)(21,24)(23,26)(25,27)(28,31,34,49)(29,36,39,55)(30,41,44,57)(32,47,33,48)(35,50,52,58)(37,54,38,45)(40,53,51,59)(42,46,43,56)

Conjugacy classes & character table

646 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 2979);