Finite Group DatabasebetaFinite Group Databasebeta| order | 2640 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Hall | (C2×D3)⋊Dic11 ⋊ C5 |
| Hall | C3×C11⋊C5 ⋊ C22⋊C4 |
| Hall | C11⋊C5 ⋊ (C2×D3)⋊C4 |
| Hall | C3×C11 ⋊ C5×C22⋊C4 |
| Sylow | C11 ⋊ C5×(C2×D3)⋊C4 |
| Sylow | C3 ⋊ C22⋊(Dic11⋊C5) |
136 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 47 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^2,5,2^2,3,11|b^2=de,b^a=bd,f^a=f^2,g^b=g^10,g^c=g^9102 conjugacy classes — view the full character table.
| maximal subgroup of | D3×C22⋊(Dic11⋊C5), #72217241, (C2×D3)⋊C4×AGL(1,𝔽11), … |
| maximal normal subgroup of | D3×C22⋊(Dic11⋊C5), #72217241, (C2×D3)⋊C4×AGL(1,𝔽11), … |
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, 5, 2, 2, 3, 11]);;
gap> SetPower(coll, 2, F.4*F.5);;
gap> SetConjugate(coll, 2, 1, F.2*F.4);;
gap> SetConjugate(coll, 6, 1, F.6^2);;
gap> SetConjugate(coll, 7, 2, F.7^10);;
gap> SetConjugate(coll, 7, 3, F.7^9);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);