Finite Group DatabasebetaFinite Group Databasebeta| order | 1536 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C3×#12826 ⋊ C2 |
| Sylow | C3 ⋊ #500743 |
2226 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 4 generators on 35 points:
(1,2,3)(6,15)(7,19)(8,20)(10,24)(11,27)(13,28)(14,25)(16,18)(17,31)(21,33)(22,32)(23,34)(26,35)(29,30);(2,3)(10,23)(14,26)(24,34)(25,35);(4,6,7,16,20,22,33,31,9,17,21,32,8,18,19,15)(5,10,11,25,28,14,30,24,12,23,29,35,13,26,27,34);(4,5)(6,14,17,26)(7,11)(8,13)(9,12)(10,22,23,18)(15,25,31,35)(16,24,32,34)(19,27)(20,28)(21,29)(30,33)Polycyclic presentation:
2^9,3|a^2=g,b^2=e,e^2=hi,h^2=i,b^a=bgh,c^a=cg,c^b=cf,d^b=def,e^d=eh,f^a=fi,g^b=gi,h^d=hi,j^c=j^290 conjugacy classes — view the full character table.
| maximal subgroup of | #72270453, #72271743 |
| maximal normal subgroup of | #72270453, #72271743 |
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", "h", "i", "j");;
gap> coll := SingleCollector(F, [2, 2, 2, 2, 2, 2, 2, 2, 2, 3]);;
gap> SetPower(coll, 1, F.7);;
gap> SetPower(coll, 2, F.5);;
gap> SetPower(coll, 5, F.8*F.9);;
gap> SetPower(coll, 8, F.9);;
gap> SetConjugate(coll, 2, 1, F.2*F.7*F.8);;
gap> SetConjugate(coll, 3, 1, F.3*F.7);;
gap> SetConjugate(coll, 3, 2, F.3*F.6);;
gap> SetConjugate(coll, 4, 2, F.4*F.5*F.6);;
gap> SetConjugate(coll, 5, 4, F.5*F.8);;
gap> SetConjugate(coll, 6, 1, F.6*F.9);;
gap> SetConjugate(coll, 7, 2, F.7*F.9);;
gap> SetConjugate(coll, 8, 4, F.8*F.9);;
gap> SetConjugate(coll, 10, 3, F.10^2);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);