Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C11 ⋊ #2085 |
214 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 214 conjugacy classes of subgroups — too many to draw. Only its 83 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1408 |
Polycyclic presentation:
2^7,11|a^2=eg,b^2=d,c^2=d,f^2=g,b^a=bd,c^a=ce,h^a=h^10,c^b=cf,f^b=fg,h^b=h^10,f^c=fg172 conjugacy classes — view the full character table.
| maximal subgroup of | D11×#2085, C2×#13070102, #14782753, … |
| maximal normal subgroup of | D11×#2085, C2×#13070102, #14782753, … |
| maximal quotient of | #14658718, #14658725, #14658732, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 5996);