%I #14 Jun 15 2024 18:00:40

%S 1,165,440,990,1584,1320,0,1980,0,0,1440

%N a(n) = number of elements of order n in simple group M_11 of order 7920.

%D J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker and R. A. Wilson, ATLAS of Finite Groups. Oxford Univ. Press, 1985 [for best online version see https://oeis.org/wiki/Welcome#Links_to_Other_Sites].

%H ATLAS, <a href="https://brauer.maths.qmul.ac.uk/Atlas/spor/M11/">Mathieu group M11</a>

%o (Magma) /* Mathieu group M11 presented on its standard generators. */

%o G<x,y>:=Group<x,y|x^2, y^4, (x*y)^11, (x*y^2)^6, x*y*x*y*x*y^-1*x*y*x*y^2*x*y^-1*x*y*x*y^-1*x*y^-1>;

%o H:= sub< G | x>;

%o f,L := CosetAction(G,H);

%o // Order(G) eq Order(L); /* 7920 = 7920*/

%o t2:=Classes(L);

%o t1:=[0 : n in [1..11]];

%o for c in t2 do t1[c[1]] := t1[c[1]] + c[2]; end for;

%o t1; /* edited by _Charles R Greathouse IV_, May 29 2015 */

%Y Cf. A284842 (M_12), A284846 (M_22), A284872 (M_23), A146074 (M_24).

%K nonn,fini,full

%O 1,2

%A _N. J. A. Sloane_, Apr 06 2009