C₃×C₉²×C₅₉ #28385015

order	14337
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	?
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₃²×C₉

Aliases

abelian

C₃×C₉²×C₅₉

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃²	C₃³×C₅₉
socle, prime radical	C₃³×C₅₉	C₃²
LCS	G ▷ C₁
UCS	C₁ ◁ G

252 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 80
transitive degree	μ_t(G) = 14337

A minimal faithful permutation representation — 3 generators on 80 points:

(1,2,3,4,5,6,7,8,9)(22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80);(10,11,12,13,14,15,16,17,18);(19,20,21)

Conjugacy classes & character table

14337 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₃×C₉²×C₅₉
maximal normal subgroup of	C₂×C₃×C₉²×C₅₉
maximal quotient of	C₂×C₃×C₉²×C₅₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14337, 31);

C3×C92×C59 #28385015