Finite Group DatabasebetaFinite Group Databasebeta| order | 4056 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Hall | C13×Dic26 ⋊ C3 |
| Hall | #92788 ⋊ Q8 |
| Sylow | C132 ⋊ C3×Q8 |
84 conjugacy classes of subgroups.
| minimal degree | μ(G) = 34 |
| transitive degree | μt(G) = 104 |
A minimal faithful permutation representation — 2 generators on 34 points:
(1,3,4,8)(2,5,6,7)(10,11,13)(12,15,18)(14,17,16)(19,21,20)(22,23,29)(24,34,26)(25,28,33)(27,30,31);(1,2,4,6)(3,7,8,5)(9,13,18,10,16,15,12,20,19,11,17,21,14)(23,25)(24,26)(27,28)(29,31)(30,32)(33,34)Polycyclic presentation:
2^2,3,2,13^2|a^2=d,b^2=d,b^a=bd,e^a=e^12,e^c=e^3,f^a=e^7f,f^c=f^3139 conjugacy classes — view the full character table.
| maximal subgroup of | #72229210, #72229416, #72259361, … |
| maximal normal subgroup of | #72229210, #72229416, #72259361, … |
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, 3, 2, 13, 13]);;
gap> SetPower(coll, 1, F.4);;
gap> SetPower(coll, 2, F.4);;
gap> SetConjugate(coll, 2, 1, F.2*F.4);;
gap> SetConjugate(coll, 5, 1, F.5^12);;
gap> SetConjugate(coll, 5, 3, F.5^3);;
gap> SetConjugate(coll, 6, 1, F.5^7*F.6);;
gap> SetConjugate(coll, 6, 3, F.6^3);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);