C₂²×C₉×C₁₉×C₂₉ #34090597

order	19836
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	?
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂

Aliases

abelian	C₂²×C₉×C₁₉×C₂₉
multiplicative	(ℤ/20957)ˣ, (ℤ/21299)ˣ, (ℤ/29781)ˣ, (ℤ/41914)ˣ, (ℤ/42598)ˣ, (ℤ/59562)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃	C₂²×C₃×C₁₉×C₂₉
socle, prime radical	C₂²×C₃×C₁₉×C₂₉	C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 61
transitive degree	μ_t(G) = 19836

A minimal faithful permutation representation — 2 generators on 61 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);(3,4)

Conjugacy classes & character table

19836 conjugacy classes. The character table is too large to display.

Relationships

automorphism group of	C₁₉×C₁₁₀₃
outer automorphism group of	C₁₉×C₁₁₀₃

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19836, 13);

C22×C9×C19×C29 #34090597