/* Group 2754990144.iv 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([22, 2, 3, 2, 2, 3, 2, 3, 2, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 52914512772, 89104925625, 20463202343, 40475209502, 67177924530, 2669236462, 210742724019, 32542802977, 315852639, 245, 178903470244, 83552016266, 34572487888, 2614306952, 246098682725, 68466347163, 160033, 10725805007, 2962539849, 379, 213814808598, 135009953260, 56170817522, 24298690488, 10548547642, 232439061895, 192006010973, 47762516787, 14708650249, 15996869951, 6030010389, 1219522267, 513, 528812805320, 138706474926, 2188552660, 31621319210, 2347157832, 3454288318, 247548644649, 165654743791, 40021201493, 35295907755, 7593719857, 3048796199, 3776683, 317747285, 647, 556407004042, 19308440480, 50331036150, 38183546092, 16576339922, 190705800, 5972, 580552676363, 8220351777, 54339994423, 157044173, 27072999459, 579909, 147499, 3377, 22826479116, 143686281058, 53765629688, 176061678, 4633300, 38548346, 1634737270, 415016504, 983478, 45244310, 202165818637, 151051557923, 109953220665, 63385084303, 16020208613, 5373932379, 1761096119, 447035085, 149272411, 8275621, 411860972174, 207395717796, 55477509178, 67669240400, 17161729302, 32717644, 1884690888, 479922490, 909032, 16140, 314756057103, 170726206501, 137203697723, 8971015761, 33707342695, 3090143357, 5407472019, 1567450537, 901568639, 84919509, 124797259, 55712705, 18571095, 6190573, 113938399888, 181867726694, 31293782844, 27905863474, 35735529560, 3257103294, 5751982516, 1661053850, 959007252, 90590494, 132778838, 59255322, 19751968, 6584198, 177203220497, 462263915559, 92088741949, 59161145555, 17585175273, 8199310015, 4551983717, 1590931755, 233836609, 78016175, 56293617, 62933371, 6992871, 35987, 12249, 778749168402, 542940387304, 104972440382, 36394190004, 44542050010, 10251028784, 2204983590, 588607708, 421211270, 240595164, 209344252, 120688, 861846, 287536, 69362, 406836587539, 72332663081, 67667529685, 311494740500, 282651659178, 93275183296, 84201495926, 43868263932, 17349937042, 3310067528, 1225601166, 448617904, 149621690, 10104180, 54898336, 6100092, 150038, 50268, 17048, 1240131036693, 351187550251, 508083905, 58531258455]); a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r := Explode([GPC.1, GPC.2, GPC.3, GPC.4, GPC.6, GPC.8, GPC.10, GPC.12, GPC.13, GPC.14, GPC.15, GPC.16, GPC.17, GPC.18, GPC.19, GPC.20, GPC.21, GPC.22]); AssignNames(~GPC, ["a", "b", "c", "d", "d2", "e", "e2", "f", "f2", "g", "g2", "h", "i", "j", "k", "l", "m", "n", "o", "p", "q", "r"]);
GPerm := PermutationGroup< 36 | (1,19,4,24,13,32,28,10,27,8,16,34,3,20,5,23,14,33,30,12,25,9,17,36,2,21,6,22,15,31,29,11,26,7,18,35), (1,33,22,17,14,21,34,29,25,7,12,5,2,32,24,18,13,20,36,28,27,9,11,6,3,31,23,16,15,19,35,30,26,8,10,4) >;

 
/* Booleans */
RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable  : BoolElt >; 
booleans_2754990144_iv := 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>;