GROUPS AND MANY-VALUED FUNCTIONS. 349 



^3=(2^(i-3r(^-3r + 3Ud.5 + ^ + ^ = 2i6543, 



^4=(2'(i-4ri«-4)' + 4)mod.5 + ^ + - = 5326i4, 



The five derived groups of (H) 



{W, + W,+ W,+ W,+ W,)li s^ie 



645231 



426531 



562431 



254631 



452361 



265341 



624351 



546321 



523641 



653421 



243561 



463251 



236451 



534261 



435621 



632541 



364521 



342651 



356241 



325461 



465132 



614532 



541632 



156432 



651342 



145362 



416352 



564312 



513462 



453612 



163542 



643152 



134652 



536142 



635412 



431562 



346512 



361452 



354162 



315642 



216543 



152643 



625143 



561243 



165423 



526413 



251463 



612453 



654213 



264153 



514623 



124563 



542163 



641523 



146253 



245613 



421653 



415263 



462513 



456123 



532614 



365214 



256314 



623514 



326154 



652134 



563124 



235164 



261534 



521364 



631254 



351624 



615324 



213654 



312564 



516234 



153264 



136524 



125634 



162354 



341265 



423165 



132465 



214365 



412635 



231645 



324615 



143625 



126345 



316425 



246135 



436215 



263415 



164235 



461325 



362145 



634125 



642315 



613245 



621435. 



