C₃×C₅₃×#732 #27166241

order	12879
nilpotency class	3
isoclinism	isoclinic class of AΣL(1,𝔽₂₇)
automorphism	?
homology	Abelianization (H₁) = C₃³×C₅₃ · Schur multiplier (H₂) = C₃⁴

Aliases

direct product

C₃×C₅₃×#732

Subgroups

	subgroup	G/H
center, socle	C₃²×C₅₃	H(3,𝔽₃)
commutator, Frattini, cosocle	C₃²	C₃³×C₅₃
LCS	G ▷ C₃² ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃²×C₅₃ ◁ C₃³×C₅₃ ◁ G

168 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 83
transitive degree	μ_t(G) = 4293

A minimal faithful permutation representation — 3 generators on 83 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);(57,58,61)(59,65,69)(60,64,70)(62,71,67)(63,74,68)(66,76,79)(72,82,83)(73,81,78)(75,80,77);(57,59,66,68,78,83,60,67,77)(58,62,72,63,65,75,64,73,76)(61,69,79,74,81,82,70,71,80)

Conjugacy classes & character table

2703 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₅₃×#10624477, C₅₃×#10624478, C₅₃×#10624480, …
maximal normal subgroup of	C₅₃×#10624477, C₅₃×#10624478, C₅₃×#10624480, …
maximal quotient of	C₃×C₅₃×#6856, C₃×C₅₃×#6859, C₃×C₅₃×#6861, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12879, 53);

C3×C53×#732 #27166241