C₃³×C₉×C₅₃ #27166249

order	12879
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	?
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₃⁶

Aliases

abelian

C₃³×C₉×C₅₃

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃	C₃⁴×C₅₃
socle, prime radical	C₃⁴×C₅₃	C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

792 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 71
transitive degree	μ_t(G) = 12879

A minimal faithful permutation representation — 4 generators on 71 points:

(1,2,3,4,5,6,7,8,9)(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);(10,11,12);(13,14,15);(16,17,18)

Conjugacy classes & character table

12879 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₅₃×#10624444, C₅₃×#10624466, C₃×C₅₃×#6855, …
maximal normal subgroup of	C₅₃×#10624444, C₅₃×#10624466, C₃×C₅₃×#6855, …
maximal quotient of	C₃²×C₉²×C₅₃, C₃²×C₅₃×C₃²⋊C₉, C₃²×C₅₃×C₉⋊C₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12879, 61);

C33×C9×C53 #27166249