Pathological speed in ConjugatorPermGroup, GAP 4.x

gistfile1.txt

G:=Group( [
(26,51,76,101)(27,52,77,102)(28,53,78,103)(29,54,79,104)(30,55,80,105)
	(31,56,81,106)(32,57,82,107)(33,58,83,108)(34,59,84,109)(35,60,85,110)
	(36,61,86,111)(37,62,87,112)(38,63,88,113)(39,64,89,114)(40,65,90,115)
	(41,66,91,116)(42,67,92,117)(43,68,93,118)(44,69,94,119)(45,70,95,120)
	(46,71,96,121)(47,72,97,122)(48,73,98,123)(49,74,99,124)(50,75,100,125),
(2,16,26,77,44,7,91,54,108,50,37,67,93,74,8,96,104,60,63,48,47,42,17,41)
	(3,21,51,103,75,13,121,80,39,57,68,98,124,85,14,106,30,87,94,59,58,73,23,71)
	(4,6,76,29,82,19,31,102,70,88,99,109,35,112,20,36,52,118,125,90,89,84,9,81)
	(5,11,101,55,113,25,61,28,97,119,110,40,62,43,22,66,78,49,32,117,120,115,15,111)
	(10,86,79,34,107,45,12,116,105,65,38,72,18,46,27,92,69,83,24,56,53,123,100,114)
	(33,122,95,64) ] );
A:=Group( [ (2,5,4,3)(6,11,16,21)(7,15,19,23)(8,12,20,24)(9,13,17,25)(10,14,18,22)
	(26,51,76,101)(27,55,79,103)(28,52,80,104)(29,53,77,105)(30,54,78,102)
	(31,61,91,121)(32,65,94,123)(33,62,95,124)(34,63,92,125)(35,64,93,122)
	(36,66,96,106)(37,70,99,108)(38,67,100,109)(39,68,97,110)(40,69,98,107)
	(41,71,81,111)(42,75,84,113)(43,72,85,114)(44,73,82,115)(45,74,83,112)
	(46,56,86,116)(47,60,89,118)(48,57,90,119)(49,58,87,120)(50,59,88,117) ] );
B:=Group( [ (2,3,4,5)(6,11,16,21)(7,13,19,25)(8,14,20,22)(9,15,17,23)(10,12,18,24)
	(26,51,76,101)(27,53,79,105)(28,54,80,102)(29,55,77,103)(30,52,78,104)
	(31,61,91,121)(32,63,94,125)(33,64,95,122)(34,65,92,123)(35,62,93,124)
	(36,66,96,106)(37,68,99,110)(38,69,100,107)(39,70,97,108)(40,67,98,109)
	(41,71,81,111)(42,73,84,115)(43,74,85,112)(44,75,82,113)(45,72,83,114)
	(46,56,86,116)(47,58,89,120)(48,59,90,117)(49,60,87,118)(50,57,88,119) ] );

# Fast:
ConjugatorPermGroup( G^(1,125), A^(1,125), B^(1,125) );
#RepresentativeAction( G^(1,125), A^(1,125), B^(1,125) );

# Slow:
ConjugatorPermGroup( G, A, B );
#RepresentativeAction(G, A, B);