C₃×C₅₃×#731 #27166240

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

Aliases

direct product

C₃×C₅₃×#731

Subgroups

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

144 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);(57,59,66,60,67,77,68,78,83)(58,62,72,64,73,76,63,65,75)(61,69,79,70,71,80,74,81,82)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₉×C₅₃×#731, C₅₃×#731⋊C₉, C₅₃×#10624731, …
maximal normal subgroup of	C₉×C₅₃×#731, C₅₃×#731⋊C₉, C₅₃×#10624731, …
maximal quotient of	C₃×C₅₃×#6857, C₃×C₅₃×#6858, C₃×C₅₃×#6859, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12879, 52);

C3×C53×#731 #27166240