C₅₃×#6869 #27166204

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

Aliases

direct product

C₅₃×#6869

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	C₃³×C₅₃	C₉
LCS	G ▷ C₃² ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₉×C₅₃ ◁ C₃×C₉×C₅₃ ◁ G

62 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 2 generators on 80 points:

(1,2,5,3,8,13,9,17,21,4,6,12,10,14,20,18,22,26,11,7,15,19,16,23,25,24,27)(28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80);(2,6,7)(8,14,16)(17,22,24)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₅₃×#10624507, C₅₃×#10624510, C₅₃×#10624511, …
maximal normal subgroup of	C₅₃×#10624507, C₅₃×#10624510, C₅₃×#10624511, …
maximal quotient of	C₅₃×#10624444, C₅₃×#10624445, C₅₃×#10624446, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12879, 16);

C53×#6869 #27166204