C₅₃×#6860 #27166195

order	12879
nilpotency class	3
isoclinism	isoclinic class of #6856
automorphism	?
homology	Abelianization (H₁) = C₃²×C₅₃ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₅₃×#6860

Subgroups

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

70 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 71
transitive degree	μ_t(G) = 4293

A minimal faithful permutation representation — 2 generators on 71 points:

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃×C₅₃×#6860, C₅₃×#10624583, C₅₃×#10624588, …
maximal normal subgroup of	C₃×C₅₃×#6860, C₅₃×#10624583, C₅₃×#10624588, …
maximal quotient of	C₅₃×#10624451, C₅₃×#10624452, C₃×C₅₃×#6860

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12879, 7);

C53×#6860 #27166195