Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C11 ⋊ #2037 |
326 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 71 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|c^2=d,e^2=g,b^a=bd,c^a=ce,e^a=eg,f^a=fg,c^b=cf,e^b=eg,e^c=eg,h^c=h^10136 conjugacy classes — view the full character table.
| maximal subgroup of | D11×#2037, C2×#13069823, #14781370, … |
| maximal normal subgroup of | D11×#2037, C2×#13069823, #14781370, … |
| maximal quotient of | #14657038, #14657045, #14657066, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 5717);