/* Group 21233664.bk downloaded from the LMFDB on 04 February 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([22, 2, 2, 3, 2, 2, 3, 2, 3, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 257621232, 608494041, 111, 891078938, 206178238, 657523683, 624903865, 112320167, 1212396244, 366605606, 109449498, 186282210, 312, 2080241861, 715432635, 230343745, 141021479, 13685875, 2364493830, 1428810796, 257465258, 27684960, 26380294, 21439226, 446, 410015239, 1139922461, 151479027, 231754057, 111011039, 54896277, 64608200, 1522350750, 44668852, 269892290, 106442520, 69653152, 29161976, 10749780, 580, 3963991689, 1548476191, 266906693, 363570315, 166684417, 47029079, 19786941, 10931083, 647, 2571085450, 679146896, 23286, 40220476, 50669090, 9269688, 24347278, 13140764, 4040036363, 1505490657, 1396289719, 122373603, 1539791, 617925, 912571, 1674497, 836583, 1396631820, 1513450258, 453528560, 139119652, 83150618, 26728560, 844438, 3864620, 142638, 303964, 368050, 848, 255467533, 1041030179, 51093561, 170844005, 4745853, 2365651, 1186649, 1180539374, 2169192996, 958894258, 326189240, 179061402, 23133454, 34499666, 1805928, 2106910, 2875172, 150714, 4238, 4686004239, 2335703077, 595330619, 12165223, 1622163, 1013929, 338111, 135381, 84715, 5277457168, 722208998, 1718316132, 245583464, 40176724, 3231530, 1095264, 475942, 274004, 9256, 5255331857, 2635877415, 513277, 27371603, 2281109, 228267, 76225, 190295, 19245, 4923224082, 36837544, 359752598, 527282004, 34670698, 45384918, 20766412, 6922274, 3782280, 1730758, 40410, 223534099, 2919723881, 443124063, 103403605, 222013547, 38142871, 7096493, 6531555, 3931177, 1627799, 229083, 6713407028, 3776927658, 125737984, 182236910, 59983416, 84228736, 23418008, 31734030, 1375108, 5510954, 870648, 137036, 165597717, 4848855307, 587798705, 434903127, 83635309, 15193881, 21187759, 7161461, 618771, 1796365, 66109]); a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p := Explode([GPC.1, GPC.2, GPC.4, GPC.5, GPC.7, GPC.9, GPC.12, GPC.13, GPC.15, GPC.16, GPC.17, GPC.18, GPC.19, GPC.20, GPC.21, GPC.22]); AssignNames(~GPC, ["a", "b", "b2", "c", "d", "d2", "e", "e2", "f", "f2", "f4", "g", "h", "h2", "i", "j", "k", "l", "m", "n", "o", "p"]);
GPerm := PermutationGroup< 24 | (1,10)(2,12,4,9)(3,11)(5,16,8,15,7,13,6,14)(17,23,18,22,20,21)(19,24), (1,20,7,24,3,17,6,23)(2,18,8,22,4,19,5,21)(9,12,11)(13,16,15), (1,18,11,7,22,14,4,17,10,5,23,16,3,19,9,8,24,13)(2,20,12,6,21,15) >;

 
/* Booleans */
RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable  : BoolElt >; 
booleans_21233664_bk := 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>;