C₁₉×#10135 #18016094

order	4864
nilpotency class	3
isoclinism	isoclinic class of #10128
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₉×#10135

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

434 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 434 conjugacy classes of subgroups — too many to draw. Only its 102 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)(22,28)(23,30)(25,33)(26,31)(29,32)(34,35)(36,37,42,47)(38,48,51,59)(39,44,55,62)(40,46,41,45)(43,52,58,50)(49,64,65,60)(53,67,66,57)(54,63,56,61);(20,21,24,27)(22,25,29,34)(23,31,30,26)(28,35,32,33)(36,38)(37,43)(39,53)(40,52)(41,50)(42,51)(44,60)(45,59)(46,48)(47,58)(49,54)(55,66)(56,65)(57,61)(62,64)(63,67);(20,22)(21,25)(23,32)(24,29)(26,35)(27,34)(28,30)(31,33)(36,39,42,55)(37,44,47,62)(38,49,51,65)(40,54,41,56)(43,57,58,67)(45,61,46,63)(48,60,59,64)(50,53,52,66)

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, 3123);