C₂²×C₅×C₇×C₁₁×C₁₃ #34093448

order	20020
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	?
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂

Aliases

abelian	C₂²×C₅×C₇×C₁₁×C₁₃
multiplicative	(ℤ/20953)ˣ, (ℤ/22033)ˣ, (ℤ/41906)ˣ, (ℤ/44066)ˣ

80 conjugacy classes of subgroups.

minimal degree	μ(G) = 40
transitive degree	μ_t(G) = 20020

A minimal faithful permutation representation — 2 generators on 40 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);(3,4)

20020 conjugacy classes. The character table is too large to display.

automorphism group of	C₂₃×C₉₁₁, C₁₁×C₂₀₀₃
outer automorphism group of	C₂₃×C₉₁₁, C₁₁×C₂₀₀₃

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20020, 25);