THE REV. T. P. KIRKMAN ON NON-MODULAR GROUPS. 213 



«j 154326 c,= 165432 

 B 214365 B = 214365 

 «* 624351 ^>, = 5236i4 

 A 564312 I =456123 



«i = 34i256 



F = 632541 



flj 154326 c,= 165432 c, = 165432 



B 351624 B = 35i624 aj = i54326 



«, 653421 6, = 2i3546 fl, = i43265 



A 456123 1=432165 e,= 132654 



fli = 62435i 63=126543 



F=5462i3 



The first found a^ is not^ but the second «, is, permu- 

 table with a^ ; wherefore B = 35 1624 is correct. 



We have aj)^j a^e^, a^c^^ aji^ a^h^ ; that is, we have the 

 remaining five quintuplets 



«i = 62435i 



«i = 62435i 



«2=65342i 



i, = 126543 



e, = 132654 



^1 = 143265 



<?,=32i465 



Cj =463152 



^5=523614 



63 = 523614 



^,=216453 



Cj =463152 



c^=^2Si3^ 



^5 = 341256 



^ = 213546 



«j = 154326 



«z=65342i 





^ = 213546 



^1= 165432 





Cz=425i36 



6,=2i6453 





<^j = 34i256 



4=321465 





e, =532416 



^1=532416. 





Next we have C=Bi,, G=Be„ 'E=¥e^, H = r</,, D = I^j, 

 J=zld^j and the whole of the twenty-five substitutions of the 

 second order; and with them the entire group of 120 are 

 determined. This is one of the non-modular groups of 

 art. 65 of my memoir above quoted. 



I do not see that this mode of investigating this group 

 of 120 adds much to our knowledge of these groups; but 



