Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C11×#340 ⋊ C2 |
| Sylow | C11 ⋊ #2023 |
326 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 87 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 704 |
Polycyclic presentation:
2^7,11|a^2=d,b^2=d,e^2=g,b^a=bd,c^a=ce,e^a=eg,c^b=cf,h^b=h^10,e^c=eg,h^c=h^10172 conjugacy classes — view the full character table.
| maximal subgroup of | D11×#2023, C2×#13069751, #14781068, … |
| maximal normal subgroup of | D11×#2023, C2×#13069751, #14781068, … |
| maximal quotient of | #14656742, #14656752, #14656782, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 5645);