Finite Group DatabasebetaFinite Group Databasebeta| order | 14280 |
| automorphism | Aut(G) order 10967040 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
| dicyclic | Dic3570 |
96 conjugacy classes of subgroups.
| minimal degree | μ(G) = 40 |
| transitive degree | μt(G) = 14280 |
A minimal faithful permutation representation — 2 generators on 40 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);(1,5,3,7)(2,6,4,8)(10,11)(13,16)(14,15)(18,23)(19,22)(20,21)(25,40)(26,39)(27,38)(28,37)(29,36)(30,35)(31,34)(32,33)Polycyclic presentation:
2^3,3,5,7,17|a^2=c,b^2=c,b^a=bc,d^a=d^2,e^a=e^4,f^a=f^6,g^a=g^163573 conjugacy classes. The character table is too large to display.
| maximal subgroup of | Dic7140, Dic10710 |
| maximal normal subgroup of | Dic7140 |
| maximal quotient of | Dic10710 |
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, 3, 5, 7, 17]);;
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.4^2);;
gap> SetConjugate(coll, 5, 1, F.5^4);;
gap> SetConjugate(coll, 6, 1, F.6^6);;
gap> SetConjugate(coll, 7, 1, F.7^16);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);