Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C11 ⋊ #1753 |
348 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 137 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=e,b^2=f,c^2=e,e^2=g,b^a=bd,c^a=cg,h^a=h^10,h^b=h^10,h^c=h^10256 conjugacy classes — view the full character table.
| maximal subgroup of | D11×#1753, C2×#13068402, #14751359, … |
| maximal normal subgroup of | D11×#1753, C2×#13068402, #14751359, … |
| maximal quotient of | #14644253, #14644259, #14644264, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 4296);