Finite Group DatabasebetaFinite Group Databasebeta| order | 53792 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
| dicyclic | Dic13448 |
| Sylow | C1681 ⋊ Q32 |
36 conjugacy classes of subgroups.
| minimal degree | μ(G) = 1713 |
| transitive degree | μt(G) = 53792 |
A minimal faithful permutation representation — 2 generators on 1713 points:
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(789,958)(790,957)(791,956)(792,955)(793,954)(794,953)(795,952)(796,951)(797,950)(798,949)(799,948)(800,947)(801,946)(802,945)(803,944)(804,943)(805,942)(806,941)(807,940)(808,939)(809,938)(810,937)(811,936)(812,935)(813,934)(814,933)(815,932)(816,931)(817,930)(818,929)(819,928)(820,927)(821,926)(822,925)(823,924)(824,923)(825,922)(826,921)(827,920)(828,919)(829,918)(830,917)(831,916)(832,915)(833,914)(834,913)(835,912)(836,911)(837,910)(838,909)(839,908)(840,907)(841,906)(842,905)(843,904)(844,903)(845,902)(846,901)(847,900)(848,899)(849,898)(850,897)(851,896)(852,895)(853,894)(854,893)(855,892)(856,891)(857,890)(858,889)(859,888)(860,887)(861,886)(862,885)(863,884)(864,883)(865,882)(866,881)(867,880)(868,879)(869,878)(870,877)(871,876)(872,875)(873,874)Polycyclic presentation:
2^5,41^2|a^2=e,b^2=cd,c^2=de,d^2=e,f^41=g,b^a=bc,c^a=cd,d^a=de,f^a=f^40g^40,g^a=g^4013451 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id. Construct it from its polycyclic presentation:
gap> F := FreeGroup(IsSyllableWordsFamily, "a", "b", "c", "d", "e", "f", "g");;
gap> coll := SingleCollector(F, [2, 2, 2, 2, 2, 41, 41]);;
gap> SetPower(coll, 1, F.5);;
gap> SetPower(coll, 2, F.3*F.4);;
gap> SetPower(coll, 3, F.4*F.5);;
gap> SetPower(coll, 4, F.5);;
gap> SetPower(coll, 6, F.7);;
gap> SetConjugate(coll, 2, 1, F.2*F.3);;
gap> SetConjugate(coll, 3, 1, F.3*F.4);;
gap> SetConjugate(coll, 4, 1, F.4*F.5);;
gap> SetConjugate(coll, 6, 1, F.6^40*F.7^40);;
gap> SetConjugate(coll, 7, 1, F.7^40);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);