C₃×C₉×C₁₉×C₂₇ #28352874

order	13851
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	?
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₃²×C₉

Aliases

abelian

C₃×C₉×C₁₉×C₂₇

Subgroups

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

404 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 58
transitive degree	μ_t(G) = 13851

A minimal faithful permutation representation — 3 generators on 58 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27)(40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58);(28,29,30,31,32,33,34,35,36);(37,38,39)

Conjugacy classes & character table

13851 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₃×C₉×C₁₉×C₂₇
maximal normal subgroup of	C₂×C₃×C₉×C₁₉×C₂₇
maximal quotient of	C₂×C₃×C₉×C₁₉×C₂₇

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13851, 238);

C3×C9×C19×C27 #28352874