C₂²×C₃²×C₅×C₇×C₁₇ #36339337

order	21420
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	?
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂×C₃

Aliases

abelian	C₂²×C₃²×C₅×C₇×C₁₇
multiplicative	(ℤ/21733)ˣ, (ℤ/24997)ˣ, (ℤ/32139)ˣ, (ℤ/43466)ˣ, (ℤ/49994)ˣ, (ℤ/64278)ˣ

240 conjugacy classes of subgroups.

minimal degree	μ(G) = 39
transitive degree	μ_t(G) = 21420

A minimal faithful permutation representation — 2 generators on 39 points:

(1,2)(5,6,7)(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);(3,4)(8,9,10)

21420 conjugacy classes. The character table is too large to display.

automorphism group of	C₁₀₃×C₂₁₁
outer automorphism group of	C₁₀₃×C₂₁₁

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21420, 169);