C₃²×C₁₉×C₈₁ #28353027

order	13851
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	?
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₃³

Aliases

abelian

C₃²×C₁₉×C₈₁

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂₇	C₃³×C₁₉
socle, prime radical	C₃³×C₁₉	C₂₇
LCS	G ▷ C₁
UCS	C₁ ◁ G

188 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 106
transitive degree	μ_t(G) = 13851

A minimal faithful permutation representation — 3 generators on 106 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81)(88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106);(82,83,84);(85,86,87)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂×C₃²×C₁₉×C₈₁
maximal normal subgroup of	C₂×C₃²×C₁₉×C₈₁
maximal quotient of	C₂×C₃²×C₁₉×C₈₁

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13851, 391);

C32×C19×C81 #28353027