C₂²×C₅×C₁₁×C₆₁ #27211841

order	13420
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	?
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂

Aliases

abelian

C₂²×C₅×C₁₁×C₆₁

Subgroups

	subgroup	G/H
center	G	C₁
commutator, Frattini	C₁	G
LCS	G ▷ C₁
UCS	C₁ ◁ G

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 81
transitive degree	μ_t(G) = 13420

A minimal faithful permutation representation — 2 generators on 81 points:

(1,2)(5,6,7,8,9)(10,11,12,13,14,15,16,17,18,19,20)(21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81);(3,4)

Conjugacy classes & character table

13420 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₄×C₅×C₁₁×C₆₁, C₂³×C₅×C₁₁×C₆₁
maximal normal subgroup of	C₂×C₄×C₅×C₁₁×C₆₁, C₂³×C₅×C₁₁×C₆₁
maximal quotient of	C₂×C₄×C₅×C₁₁×C₆₁, C₂³×C₅×C₁₁×C₆₁

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13420, 33);

C22×C5×C11×C61 #27211841