C₁₉×#10210 #18016169

order	4864
nilpotency class	3
isoclinism	isoclinic class of #10208
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₉×#10210

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	#392
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
prime radical	C₁₉×#532	C₂²
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

440 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 94 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) = 1216

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)(22,29)(23,24)(26,30)(27,33)(31,32)(34,35)(36,37)(38,48)(39,53)(40,46)(41,45)(42,47)(43,50)(44,54)(49,60)(51,59)(52,58)(55,62)(56,61)(57,65)(63,64)(66,67);(20,21)(22,30)(23,27)(24,33)(25,28)(26,32)(29,34)(31,35)(36,38,42,52)(37,43,47,59)(39,49,55,65)(40,51,41,50)(44,60,61,57)(45,58,46,48)(53,63,62,67)(54,66,56,64);(20,22)(21,26)(23,32)(24,29)(25,31)(27,35)(28,34)(30,33)(36,39,42,55)(37,44,47,61)(38,49,52,65)(40,54,41,56)(43,57,59,60)(45,53,46,62)(48,63,58,67)(50,64,51,66)

Conjugacy classes & character table

475 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 3198);