#gap_pyraminx.txt
#permutation sommet
pG := (30,28,29);
pD := (33,31,32);
pH := (27,25,26);
pP := (35,34,36);
#per tranche: (arete)(arete)(centre)
pg := (2,4,11)(8,10,5)(21,15,16);
pd := (1,12,4)(7,6,10)(17,14,24);
ph := (1,8,9)(7,2,3)(22,13,20);
pp := (3,5,12)(9,11,6)(23,19,18);
#permutations étendues (violer les lois)
pGamma := (1,7);
pOmega := (1,2)(7,8);
LAMBDAPLUS :=  Group( pG, pD, pH, pP, pg, pd, ph, pp, pGamma, pOmega );
LAMBDA := Group( pG, pD, pH, pP, pg, pd, ph, pp);

N := 2*2 ;; 
Print( "\n" );
Print( "|LAMBDA+| = ",Size( LAMBDAPLUS ), "\n" );
Print( "|LAMBDA| = ", Size( LAMBDA ) , "\n" );
Print( "N = ",N  , "\n" );
Print( "|G+| = ",  Factorial(6) * (2^6) * (3^4) *(3^4), "\n" );
Print( "|G| = |G+|/N = ", (Factorial(6) * (2^6)*(3^4)*(3^4)) / N, "\n" );

#Order(pG*pG*pG); 
#Order(pg*pd*pg^-1*pd^-1);
#Order(pg*pd);