Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C11 ⋊ #1845 |
280 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 149 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=f,b^2=dg,c^2=e,d^2=g,b^a=bd,c^a=ce,d^a=dg,h^b=h^10184 conjugacy classes — view the full character table.
| maximal subgroup of | #14641187, #14646825, #14646826, … |
| maximal normal subgroup of | #14641187, #14646825, #14646826, … |
| maximal quotient of | #14647513, #14647528, #14647542, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 4669);