Finite Group DatabasebetaFinite Group Databasebeta| order | 41272 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
| dicyclic | Dic10318 |
| Hall | C7×C11×C67 ⋊ Q8 |
| Hall | C11×C67 ⋊ Dic14 |
| Hall | C7×C67 ⋊ Dic22 |
| Hall | C7×C11 ⋊ Dic134 |
| Sylow | C67 ⋊ Dic154 |
| Sylow | C11 ⋊ Dic938 |
| Sylow | C7 ⋊ Dic1474 |
48 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 41272 |
A minimal faithful permutation representation — 2 generators on 93 points:
(1,2,3,4)(5,8,7,6)(9,10,11,12,13,14,15)(16,17,18,19,20,21,22,23,24,25,26)(27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93);(1,5,3,7)(2,6,4,8)(10,15)(11,14)(12,13)(17,26)(18,25)(19,24)(20,23)(21,22)(28,93)(29,92)(30,91)(31,90)(32,89)(33,88)(34,87)(35,86)(36,85)(37,84)(38,83)(39,82)(40,81)(41,80)(42,79)(43,78)(44,77)(45,76)(46,75)(47,74)(48,73)(49,72)(50,71)(51,70)(52,69)(53,68)(54,67)(55,66)(56,65)(57,64)(58,63)(59,62)(60,61)Polycyclic presentation:
2^3,7,11,67|a^2=c,b^2=c,b^a=bc,d^a=d^6,e^a=e^10,f^a=f^6610321 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");;
gap> coll := SingleCollector(F, [2, 2, 2, 7, 11, 67]);;
gap> SetPower(coll, 1, F.3);;
gap> SetPower(coll, 2, F.3);;
gap> SetConjugate(coll, 2, 1, F.2*F.3);;
gap> SetConjugate(coll, 4, 1, F.4^6);;
gap> SetConjugate(coll, 5, 1, F.5^10);;
gap> SetConjugate(coll, 6, 1, F.6^66);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);