C₂²×C₃×C₅×C₁₁×C₃₁ #35205677

order	20460
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	?
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂

Aliases

abelian	C₂²×C₃×C₅×C₁₁×C₃₁
multiplicative	(ℤ/20837)ˣ, (ℤ/21173)ˣ, (ℤ/22103)ˣ, (ℤ/41674)ˣ, (ℤ/42346)ˣ, (ℤ/44206)ˣ

Subgroups

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

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 54
transitive degree	μ_t(G) = 20460

A minimal faithful permutation representation — 2 generators on 54 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);(3,4)

Conjugacy classes & character table

20460 conjugacy classes. The character table is too large to display.

Relationships

automorphism group of	C₆₇×C₃₁₁, C₃₁×C₆₈₃
outer automorphism group of	C₆₇×C₃₁₁, C₃₁×C₆₈₃

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20460, 97);

C22×C3×C5×C11×C31 #35205677