/* Group 56623104.o downloaded from the LMFDB on 29 October 2025. */
 
/* Various presentations of this group are stored in this file: 
	 GPC is polycyclic presentation GPerm is permutation group 
	 GLZ, GLFp, GLZA, GLZq, GLFq if they exist are matrix groups 
 
 Many characteristics of the group are stored as booleans in a record: 
	 Agroup, Zgroup, abelian, almost_simple,cyclic, metabelian, 
	 metacyclic, monomial, nilpotent, perfect, quasisimple, rational, 
	 solvable, supersolvable 
 
*/
 
/* Constructions */
GPC := PCGroup([24, 2, 2, 2, 2, 2, 3, 2, 3, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 594094656, 252347617, 632655385, 1442, 570635594, 194, 4063786755, 2666166171, 2115738244, 2359421788, 1037683732, 165270556, 340, 6180042245, 991226909, 861531317, 122959949, 7279050246, 3347793822, 480255606, 1076449326, 333724710, 294813414, 486, 849825799, 1784973343, 228280375, 1118089807, 46453351, 173851903, 4386763016, 5736438176, 1019765432, 453885200, 386167928, 118990424, 104790824, 19269752, 632, 70318089, 1629342753, 1503855417, 1512933201, 583960425, 79635009, 88476633, 30967377, 2893245706, 3720055714, 3455540410, 114154, 85666, 9741754, 68129602, 22710010, 812026, 14092434443, 6599771171, 789067067, 186731, 31235, 31871387, 26552627, 8851019, 2656163, 6348865548, 6348865572, 207028284, 819217260, 70222596, 43265820, 21610548, 12703703053, 6918524965, 3079544893, 688601197, 488726917, 52690333, 26393653, 8789965, 7749733, 15034429454, 6760765478, 5062487102, 629234030, 119595014, 11353118, 5780342, 19941326, 12182630, 6863781903, 4833312807, 388841535, 519229551, 129558663, 16644255, 8101047, 21307599, 13013223, 14709620752, 8753578024, 2556417088, 14100592, 547098760, 62982304, 31021240, 10183888, 15119080, 20161363985, 5000030273, 978283121, 200061065, 192098465, 97044665, 10948817, 16091369, 3252731922, 3032100906, 3994997826, 579944562, 113467530, 193314978, 98758842, 32919762, 16109802, 20191887379, 8576409643, 4203601987, 583925875, 398131339, 172523683, 81838267, 27279571, 14377195, 3602092052, 9047033900, 989356100, 557383796, 111476876, 278692004, 130056380, 43352276, 23224556, 94887957, 7580086317, 4738922565, 1634992245, 175177869, 175177893, 107053245, 35684565, 14598381, 15872163862, 7875035182, 116370502, 854655094, 732561550, 244187302, 81395902, 27132118, 20349166, 382205975, 8281129007, 5137883207, 1274019959, 254804111, 84934823, 127402175, 42467543, 7078127]); a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s,t := Explode([GPC.1, GPC.2, GPC.3, GPC.5, GPC.7, GPC.9, GPC.11, GPC.12, GPC.13, GPC.14, GPC.15, GPC.16, GPC.17, GPC.18, GPC.19, GPC.20, GPC.21, GPC.22, GPC.23, GPC.24]); AssignNames(~GPC, ["a", "b", "c", "c2", "d", "d2", "e", "e2", "f", "f2", "g", "h", "i", "j", "k", "l", "m", "n", "o", "p", "q", "r", "s", "t"]);
GPerm := PermutationGroup< 36 | (1,19,2,20)(3,24,4,23)(5,21)(6,22)(7,17)(8,18)(9,15,10,16)(11,14,12,13)(25,31,26,32)(27,36,28,35)(29,33,30,34), (1,21,17,9,2,22,18,10)(3,20,13,8)(4,19,14,7)(5,23,16,12,6,24,15,11)(25,34,26,33)(27,31,28,32)(29,35)(30,36), (1,31,2,32)(3,35)(4,36)(5,33,6,34)(7,16)(8,15)(9,13,10,14)(11,18)(12,17)(19,27)(20,28)(21,26,22,25)(23,29)(24,30) >;

 
/* Booleans */
RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable  : BoolElt >; 
booleans_56623104_o := rec< RF |  
Agroup := false,
Zgroup := false,
abelian := false,
almost_simple := false,
cyclic := false,
metabelian := false,
metacyclic := false,
nilpotent := false,
perfect := false,
quasisimple := false,
rational := false,
solvable := true,
supersolvable := false>;