C₅₃×#6872 #27166207

order	12879
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₃×C₉×C₅₃ · Schur multiplier (H₂) = C₃

Aliases

direct product

C₅₃×#6872

Subgroups

	subgroup	G/H
center	C₉×C₅₃	H(3,𝔽₃)
commutator	C₃²	C₃×C₉×C₅₃
Frattini, cosocle	C₃×C₉	C₃²×C₅₃
socle	C₃×C₅₃	C₃²⋊C₉
prime radical	H(3,𝔽₃)×C₅₃	C₉
LCS	G ▷ C₃² ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₉×C₅₃ ◁ C₃×C₉×C₅₃ ◁ G

52 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 134
transitive degree	μ_t(G) = 4293

A minimal faithful permutation representation — 2 generators on 134 points:

(1,2,6,4,9,21,16,27,43,5,10,20,17,28,42,38,52,65,18,8,24,39,26,48,62,51,69)(3,11,29,14,31,54,36,56,73,15,25,47,37,50,68,61,71,79,13,7,19,35,23,41,60,46,64)(12,30,40,33,55,63,58,74,77,32,49,53,57,70,72,75,80,81,34,22,44,59,45,66,76,67,78)(82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134);(1,3,12)(2,7,22)(4,14,33)(5,15,32)(6,19,40)(8,25,49)(9,23,45)(10,11,30)(13,34,18)(16,36,58)(17,37,57)(20,29,53)(21,41,63)(24,47,44)(26,50,70)(27,46,67)(28,31,55)(35,59,39)(38,61,75)(42,54,72)(43,64,77)(48,68,66)(51,71,80)(52,56,74)(60,76,62)(65,73,81)(69,79,78)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃×C₅₃×#6872, C₅₃×#10624702, C₅₃×#10624724, …
maximal normal subgroup of	C₃×C₅₃×#6872, C₅₃×#10624702, C₅₃×#10624724, …
maximal quotient of	C₅₃×H(3,𝔽₃)⋊C₂₇, C₅₃×3₋¹⁺²⋊C₂₇, C₅₃×#10624453, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12879, 19);

C53×#6872 #27166207