Template:Full octahedral group; text matrices

S4 based identifiers 0 1 2 3 4 5 23' 22' 21' 20' 19' 18' 16' 17' 13' 12' 15' 14' 7 6 10 11 8 9 7' 6' 10' 11' 8' 9' 16 17 13 12 15 14 23 22 21 20 19 18 0' 1' 2' 3' 4' 5'

Reverse colexicographic ranks 0 722 288 2210 1032 2354 5167 6490 5455 7978 6936 8258 11536 10213 12096 14018 10615 13738 16703 15981 17263 19786 16519 19642 23616 24338 23056 20533 23800 20677 28783 30106 28223 26301 29704 26581 35152 33829 34864 32341 33383 32061 40319 39597 40031 38109 39287 37965

Inversion numbers 0 2 4 6 6 8 4 6 8 10 10 12 8 6 12 14 10 12 12 10 16 18 14 16 16 18 12 10 14 12 20 22 16 14 18 16 24 22 20 18 18 16 28 26 24 22 22 20

Left inversion counts 00000000 00100010 00002200 00102030 00003210 00103130 01010101 00210021 01012301 00212041 00004321 00104241 00220022 01020102 00004422 00104252 01012402 00212052 01230123 01130113 01014523 00214263 01013513 00213163 00004444 00104454 00220044 01020304 00221054 01021404 01014545 00214465 01230145 01130315 00222165 01022515 00224466 01024546 00222266 01022526 01230246 01130326 01234567 01134557 01232367 01132537 01231357 01131437