/* Group 22674816.mj downloaded from the LMFDB on 19 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([18, 2, 3, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 36, 1679635, 555220334, 292450358, 146, 814548963, 552531909, 109755705, 540771124, 140746702, 291605440, 78564118, 256, 1427264069, 992655671, 31362377, 137729003, 28942367, 1298977350, 968460216, 421241226, 80104812, 52837926, 34423548, 1351842, 2239411975, 228690457, 178789291, 177591229, 5941519, 1824289, 1584403, 421, 3346168328, 445969178, 205213868, 357758, 37332656, 18478466, 13082588, 1338596, 3280988169, 725787, 613993005, 307008063, 153530001, 34659, 9990117, 8775, 711, 1053119242, 3079342, 87760000, 43880050, 28612, 14374, 7264, 2302193675, 2208135197, 82991, 192596033, 559955, 886565, 46236215, 23013209, 221825, 2518304268, 25474206, 798490416, 211476162, 104828340, 99773958, 26535720, 13002582, 930, 223388977, 429141955, 214571029, 490009, 2218026254, 1360488992, 394865330, 5326646, 75096824, 7105442, 11547500, 7086038, 9932, 87710, 5455392783, 3063619617, 340402227, 515082309, 271019607, 114794601, 2820219, 29958477, 15959103, 979953, 28725, 197223, 2512705552, 2013019810, 947199796, 7314694, 5948728, 65479210, 914452, 16656334, 10484638, 77326, 129670, 6622166033, 1103881013, 5132231, 2612825, 86920235, 51018461, 30705623]); a,b,c,d,e,f,g,h,i,j,k,l := Explode([GPC.1, GPC.3, GPC.5, GPC.7, GPC.8, GPC.10, GPC.12, GPC.13, GPC.15, GPC.16, GPC.17, GPC.18]); AssignNames(~GPC, ["a", "a2", "b", "b2", "c", "c2", "d", "e", "e2", "f", "f3", "g", "h", "h3", "i", "j", "k", "l"]);
GPerm := PermutationGroup< 36 | (1,2)(4,35,16,24,29,12,6,36,18,22,28,10,5,34,17,23,30,11)(7,9,8)(13,27,15,25,14,26)(19,20,21), (1,29,9,12,27,18,32,24,14,5,21,35,3,30,7,11,26,16,33,23,13,6,19,34,2,28,8,10,25,17,31,22,15,4,20,36), (1,12,27,23,13,35,3,11,26,22,15,34,2,10,25,24,14,36)(4,9,18,20,29,33,6,8,17,19,28,32,5,7,16,21,30,31) >;

 
/* Booleans */
RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable  : BoolElt >; 
booleans_22674816_mj := 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>;