C₁₉×#10517 #18016476

order	4864
nilpotency class	3
isoclinism	isoclinic class of #10512
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₉×#10517

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	#394
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

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

normal subgroups only

This group has 344 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)(20,21)(22,30)(23,28)(24,27)(25,29)(26,32)(31,35)(33,34)(36,37,41,45)(38,46,49,61)(39,50,53,43)(40,54,56,44)(42,55,58,48)(47,63,51,62)(52,60,67,65)(57,64,59,66);(20,22)(21,26)(23,32)(24,33)(25,31)(27,35)(28,30)(29,34)(36,38,41,49)(37,42,45,58)(39,51,53,47)(40,55,56,48)(43,59,50,57)(44,61,54,46)(52,64,67,66)(60,62,65,63);(21,27)(22,31)(24,25)(28,29)(32,33)(34,35)(36,39,40,52,41,53,56,67)(37,43,44,60,45,50,54,65)(38,47,48,64,49,51,55,66)(42,57,46,62,58,59,61,63)

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, 3505);