C₅₃×#6911 #27166246

order	12879
nilpotency class	3
isoclinism	isoclinic class of #6909
automorphism	?
homology	Abelianization (H₁) = C₃³×C₅₃ · Schur multiplier (H₂) = C₃⁴

Aliases

direct product

C₅₃×#6911

Subgroups

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

160 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 80
transitive degree	μ_t(G) = 1431

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

(1,2,5)(3,9,14)(4,8,15)(6,16,12)(7,19,13)(10,21,24)(11,18,25)(17,27,23)(20,26,22)(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);(1,3,10,13,11,23,4,12,22)(2,6,17,7,9,20,8,18,21)(5,14,24,19,25,27,15,16,26);(3,11,12)(6,9,18)(10,22,23)(14,25,16)(17,21,20)(24,26,27)

Conjugacy classes & character table

1855 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₅₃×UT(4,𝔽₃), C₅₃×#10624749, C₅₃×#10624751, …
maximal normal subgroup of	C₅₃×UT(4,𝔽₃), C₅₃×#10624749, C₅₃×#10624751, …
maximal quotient of	C₅₃×#10624589, C₅₃×#10624596, C₅₃×#10624602, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12879, 58);

C53×#6911 #27166246