Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Sylow | C11 ⋊ #1779 |
852 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 852 conjugacy classes of subgroups — too many to draw. Only its 197 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:
2^7,11|a^2=f,f^2=g,b^a=bd,c^a=ce,h^a=h^10376 conjugacy classes — view the full character table.
| maximal subgroup of | #14640343, #14640344, #14640350, … |
| maximal normal subgroup of | #14640343, #14640344, #14640350, … |
| maximal quotient of | #14645100, #14645103, #14645107, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 4420);