# Black box algorithm to find standard generators of M12.2

	set K 0
	set L 0
	set X 0
lbl ELT2BAND12
	rand 1
	ord 1 A
	incr X
	if X gt 1000 then timeout
	if A notin 1 2 3 4 5 6 8 10 11 12 then fail
	if K eq 0 then
		if A eq 8 then
			pwr 4 1 2        # g2 is in 2B
			set K 1
		endif
	endif
	if L eq 0 then
		if A eq 12 then
			cp 1 3           # g3 has order 12
			set L 1
		endif
	endif

	if K eq 0 then jmp ELT2BAND12
	if L eq 0 then jmp ELT2BAND12

	set X 0
lbl ELT2C
	incr X
	if X gt 1000 then timeout
	rand 4
	cjr 3 4
	mu 2 3 5
	ord 5 D
	if D notin 2 4 6 10 12 then fail
	if D notin 2 6 10 then jmp ELT2C

	div D 2 E
	pwr E 5 6           # g6 is in 2C

	set X 0
lbl ELT3A
	incr X
	if X gt 1000 then timeout
	rand 7
	cjr 2 7
	mu 6 2 8
	ord 8 F
	if F notin 2 4 6 10 12 then fail
	if F noteq 12 then jmp ELT3A
	pwr 4 8 9           # g9 is in 3A

	set X 0
lbl CONJUGATE
	incr X
	if X gt 1000 then timeout

	rand 10
	cjr 9 10
	mu 6 9 11
	ord 11 G
	if G notin 2 4 6 10 12 then fail
	if G noteq 12 then jmp CONJUGATE

	mu 11 9 12
	mu 11 12 13
	ord 13 H

	if H notin 5 6 11 then fail
	if H noteq 11 then jmp CONJUGATE

	oup 2 6 9
