C₅₃×#6908 #27166243

order	12879
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₃³×C₅₃ · Schur multiplier (H₂) = C₃³

Aliases

direct product

C₅₃×#6908

Subgroups

	subgroup	G/H
center	C₉×C₅₃	H(3,𝔽₃)
commutator, Frattini, cosocle	C₃²	C₃³×C₅₃
socle	C₃×C₅₃	C₃×H(3,𝔽₃)
LCS	G ▷ C₃² ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₉×C₅₃ ◁ C₃×C₉×C₅₃ ◁ G

134 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)(3,7,12)(4,6,13)(8,17,11)(9,15,20)(10,14,21)(16,24,19)(18,22,26)(23,27,25)(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);(2,6,8)(7,14,16)(15,22,23);(1,3,9,4,10,18,11,19,25)(2,7,15,6,14,22,8,16,23)(5,12,20,13,21,26,17,24,27)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₅₃×#10624526, C₅₃×#10624530, C₅₃×#10624724, …
maximal normal subgroup of	C₅₃×#10624526, C₅₃×#10624530, C₅₃×#10624724, …
maximal quotient of	C₅₃×#10624583, C₅₃×#10624585, C₅₃×#10624587, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12879, 55);

C53×#6908 #27166243