C₂²×C₅²×C₁₁×C₁₇ #34035182

order	18700
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	?
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂×C₅

Aliases

abelian	C₂²×C₅²×C₁₁×C₁₇
multiplicative	(ℤ/20581)ˣ, (ℤ/41162)ˣ

160 conjugacy classes of subgroups.

minimal degree	μ(G) = 42
transitive degree	μ_t(G) = 18700

A minimal faithful permutation representation — 2 generators on 42 points:

(1,2)(5,6,7,8,9)(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);(3,4)(10,11,12,13,14)

18700 conjugacy classes. The character table is too large to display.

automorphism group of	C₁₁×C₁₈₇₁
outer automorphism group of	C₁₁×C₁₈₇₁

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18700, 67);