C₁₉×#10121 #18016080

order	4864
nilpotency class	3
isoclinism	isoclinic class of #10120
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₉×#10121

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	#392
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
prime radical	C₁₉×#3153	C₂
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

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

normal subgroups only

This group has 544 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) = 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)(30,39)(31,44)(32,49)(33,37)(34,38)(35,41)(36,47)(40,57)(42,52)(43,51)(45,56)(46,55)(48,54)(50,58)(53,59);(22,26)(24,27)(28,30)(29,35)(31,45)(32,42)(33,41)(34,43)(36,53)(37,51)(38,52)(39,49)(40,46)(44,50)(47,58)(48,59)(54,57)(55,56);(20,21)(22,27)(23,25)(24,26)(28,31,34,48)(29,36,38,55)(30,40,43,58)(32,46,33,47)(35,50,52,57)(37,54,49,44)(39,56,51,53)(41,45,42,59)

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, 3109);