Finite Group DatabasebetaFinite Group Databasebeta| order | 3520 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C5 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C11×2−1+4 ⋊ C2×C5 |
| Hall | #10623368 ⋊ C5 |
| Hall | C11⋊C5 ⋊ #577 |
| Sylow | C11 ⋊ C5×#577 |
516 conjugacy classes of subgroups; only the 186 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 186 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 176 |
Polycyclic presentation:
2^4,5,2^2,11|a^2=f,f^2=g,b^a=bfg,d^a=dg,d^c=dg,f^b=fg,h^a=h^10,h^b=h^10,h^e=h^9127 conjugacy classes — view the full character table.
| maximal subgroup of | #72269585, #577×AGL(1,𝔽11), #72269596 |
| maximal normal subgroup of | #72269585, #577×AGL(1,𝔽11), #72269596 |
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, 2, 5, 2, 2, 11]);;
gap> SetPower(coll, 1, F.6);;
gap> SetPower(coll, 6, F.7);;
gap> SetConjugate(coll, 2, 1, F.2*F.6*F.7);;
gap> SetConjugate(coll, 4, 1, F.4*F.7);;
gap> SetConjugate(coll, 4, 3, F.4*F.7);;
gap> SetConjugate(coll, 6, 2, F.6*F.7);;
gap> SetConjugate(coll, 8, 1, F.8^10);;
gap> SetConjugate(coll, 8, 2, F.8^10);;
gap> SetConjugate(coll, 8, 5, F.8^9);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);