/* Group 344373768.bn downloaded from the LMFDB on 24 July 2026. */
 
/* 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([19, 3, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 1568423172, 229, 741257660, 15660192827, 5862381963, 154, 1459598547, 1948932774, 212, 24398286844, 9938740423, 13534532357, 2173371720, 797587, 2528362970, 1443690153, 26233413702, 8204502961, 3896021180, 372060381, 1404261829, 392460890, 194689776, 40662628999, 2716592666, 3818321517, 1584061072, 1604799515, 365754054, 17980201, 65302988, 1421383472, 5239092555, 9749975446, 4667703959, 437774790, 571441576, 177165185, 79831662, 5975168649, 3483999628, 5565568967, 2802446106, 710694895, 802019174, 256110243, 13822, 31043501, 6505020, 68377620442, 20663211389, 2507919792, 362843713, 1508780282, 539950560, 131047513, 2024, 16951107, 7156132, 2385308, 63530943275, 13476737118, 2187927265, 5752509836, 2102526483, 469475134, 129079133, 106792380, 28395055, 12400418, 13197, 904, 38426884716, 10254948007, 5043204554, 34856429341, 23571151664, 8216524059, 2603877262, 594540432, 389961181, 50547062, 16913775, 5616508, 1872311, 814182, 54713666174, 2917020633, 7167338512, 5635833461, 17867937, 1108246, 1985495, 661974, 246463, 80716093071, 2747447458, 5179313717, 47869128, 1299113102, 231810465, 144346036, 37034663, 16038618, 5346349, 1600784, 98170901656, 33945550667, 16361816994, 2759202379, 25901519, 14913078, 2878117, 959516, 33721755425, 20594331684, 1687384279, 4424895938, 943918060, 379462127, 84934482, 28644037, 9437336, 3145923, 1292986, 43216560522, 2387469205, 14715006968, 7285570671, 106846765, 23597657, 11872035, 3957490, 1394048]); a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p := Explode([GPC.1, GPC.2, GPC.3, GPC.6, GPC.7, GPC.8, GPC.9, GPC.10, GPC.11, GPC.12, GPC.14, GPC.15, GPC.16, GPC.17, GPC.18, GPC.19]); AssignNames(~GPC, ["a", "b", "c", "c2", "c4", "d", "e", "f", "g", "h", "i", "j", "j3", "k", "l", "m", "n", "o", "p"]);
GPerm := PermutationGroup< 36 | (1,22,32)(2,23,31)(3,24,33)(4,6,5)(7,13,34,21,27,11,8,15,36,19,26,10,9,14,35,20,25,12)(16,30)(17,28)(18,29), (1,8,30,25,20,17,2,7,29,26,19,16,3,9,28,27,21,18)(4,13,31,6,14,33,5,15,32)(10,12,11)(22,36,24,35,23,34) >;

 
/* Booleans */
RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable  : BoolElt >; 
booleans_344373768_bn := 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>;