C₁₉×#10127 #18016086

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

Aliases

direct product

C₁₉×#10127

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	#392
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
prime radical	C₂³×C₁₉	#121
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

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

normal subgroups only

This group has 420 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) = 67
transitive degree	μ_t(G) = 2432

A minimal faithful permutation representation — 3 generators on 67 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,25,22)(23,30,31,35)(24,29,34,27)(26,33,28,32)(36,37)(38,47)(39,52)(40,57)(41,45)(42,46)(43,49)(44,55)(48,65)(50,60)(51,59)(53,64)(54,63)(56,62)(58,66)(61,67);(20,22,25,21)(23,28,31,26)(24,27,34,29)(30,33,35,32)(36,38)(37,43)(39,53)(40,50)(41,49)(42,51)(44,61)(45,59)(46,60)(47,57)(48,54)(52,58)(55,66)(56,67)(62,65)(63,64);(20,23)(21,26)(22,28)(24,33)(25,31)(27,35)(29,30)(32,34)(36,39,42,56)(37,44,46,63)(38,48,51,66)(40,54,41,55)(43,58,60,65)(45,62,57,52)(47,64,59,61)(49,53,50,67)

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, 3115);