C₁₉×#10339 #18016298

order	4864
nilpotency class	3
isoclinism	isoclinic class of #10336
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₉×#10339

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	#392
commutator, Frattini, cosocle	C₂⁵	C₂³×C₁₉
prime radical	C₂⁵×C₁₉	C₂³
LCS	G ▷ C₂⁵ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂⁵×C₁₉ ◁ G

738 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 738 conjugacy classes of subgroups — too many to draw. Only its 106 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) = 51
transitive degree	μ_t(G) = 608

A minimal faithful permutation representation — 3 generators on 51 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,24,29)(22,26,33,40)(23,27,34,42)(25,30,36,28)(31,45,46,41)(32,38,48,39)(35,44,49,43)(37,50,51,47);(20,22,24,33)(21,26,29,40)(23,31,34,46)(25,32,36,48)(27,41,42,45)(28,39,30,38)(35,47,49,50)(37,44,51,43);(20,23,25,35)(21,27,30,44)(22,31,32,47)(24,34,36,49)(26,37,38,45)(28,43,29,42)(33,46,48,50)(39,41,40,51)

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, 3327);