Finite Group DatabasebetaFinite Group Databasebeta| order | 3520 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C11×#106 ⋊ C2×C5 |
| Hall | #10622482 ⋊ C5 |
| Hall | C11⋊C5 ⋊ #442 |
| Sylow | C11 ⋊ C5×#442 |
264 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 84 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 352 |
Polycyclic presentation:
2^3,5,2^3,11|a^2=e,b^2=e,c^2=f,f^2=g,c^a=cf,c^b=cg,f^a=fg,h^b=h^10,h^d=h^9124 conjugacy classes — view the full character table.
| maximal subgroup of | #442×AGL(1,𝔽11), #72248784, #72248790, … |
| maximal normal subgroup of | #442×AGL(1,𝔽11), #72248784, #72248790, … |
| maximal quotient of | #72248784 |
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");;
gap> coll := SingleCollector(F, [2, 2, 2, 5, 2, 2, 2, 11]);;
gap> SetPower(coll, 1, F.5);;
gap> SetPower(coll, 2, F.5);;
gap> SetPower(coll, 3, F.6);;
gap> SetPower(coll, 6, F.7);;
gap> SetConjugate(coll, 3, 1, F.3*F.6);;
gap> SetConjugate(coll, 3, 2, F.3*F.7);;
gap> SetConjugate(coll, 6, 1, F.6*F.7);;
gap> SetConjugate(coll, 8, 2, F.8^10);;
gap> SetConjugate(coll, 8, 4, F.8^9);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);