C₃×C₁₉×#6879 #28353031

order	13851
nilpotency class	4
isoclinism	isoclinic class of #6878
automorphism	?
homology	Abelianization (H₁) = C₃³×C₁₉ · Schur multiplier (H₂) = C₃³×C₉

Aliases

direct product

C₃×C₁₉×#6879

Subgroups

	subgroup	G/H
center, socle	C₃²×C₁₉	#732
commutator, Frattini, cosocle	C₃×C₉	C₃³×C₁₉
LCS	G ▷ C₃×C₉ ▷ C₃² ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃²×C₁₉ ◁ C₃³×C₁₉ ◁ C₃²×C₉×C₁₉ ◁ G

260 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 49
transitive degree	μ_t(G) = 1539

A minimal faithful permutation representation — 3 generators on 49 points:

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

Conjugacy classes & character table

1995 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13851, 395);

C3×C19×#6879 #28353031

Aliases

Subgroups

Presentation

Conjugacy classes & character table

GAP

C₃×C₁₉×#6879 #28353031