/* Group 2834352.ot downloaded from the LMFDB on 21 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([15, 2, 2, 2, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 30, 5387056, 114755222, 53921267, 122, 140668803, 71383938, 23391904, 89801119, 28255084, 19796674, 214, 24533285, 69852260, 22591475, 22448930, 3739850, 51065286, 75781461, 70746516, 1544181, 3019026, 1686276, 411, 226748167, 25957, 56907368, 157347383, 48507698, 16161983, 13469558, 5386178, 1007333, 299196009, 86378424, 18662439, 510354, 3623469, 2967384, 1134099, 113979, 594, 190531450, 1924585, 962320, 160450, 243622091, 7348346, 87130121, 7348391, 2434961, 270671, 45506, 2442972, 204703227, 10235202, 8529372, 117754573, 287854588, 127983283, 2865313, 1379788, 799573, 361123, 68188, 194414, 106288244, 17714774]); a,b,c,d,e,f,g,h,i,j := Explode([GPC.1, GPC.3, GPC.5, GPC.7, GPC.9, GPC.10, GPC.12, GPC.13, GPC.14, GPC.15]); AssignNames(~GPC, ["a", "a2", "b", "b2", "c", "c2", "d", "d3", "e", "f", "f3", "g", "h", "i", "j"]);
GPerm := PermutationGroup< 36 | (1,17,21,12,13,28,31,24,25,6,7,35,2,16,20,10,15,30,32,23,26,4,9,36,3,18,19,11,14,29,33,22,27,5,8,34), (1,21,13,8,26,33,3,20,14,7,25,31,2,19,15,9,27,32)(4,36,17,10,29,23,5,34,16,11,28,22,6,35,18,12,30,24) >;

 
/* Booleans */
RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable  : BoolElt >; 
booleans_2834352_ot := 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>;