C₃×C₅₃×AΣL(1,𝔽₂₇) #27166239

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×AΣL(1,𝔽₂₇)

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

252 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 65
transitive degree	μ_t(G) = 1431

A minimal faithful permutation representation — 3 generators on 65 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);(57,58,60)(59,61,64)(62,65,63);(58,61,62)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₉×C₅₃×AΣL(1,𝔽₂₇), C₅₃×AΣL(1,𝔽₂₇)⋊C₉, C₅₃×#10624730, …
maximal normal subgroup of	C₉×C₅₃×AΣL(1,𝔽₂₇), C₅₃×AΣL(1,𝔽₂₇)⋊C₉, C₅₃×#10624730, …
maximal quotient of	C₃×C₅₃×#6856, C₃×C₅₃×#6857, C₃×C₅₃×#6858, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12879, 51);

C3×C53×AΣL(1,𝔽27) #27166239