Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C11 ⋊ #2208 |
166 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 51 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=g,b^2=d,e^2=fg,f^2=g,b^a=bd,c^a=ce,e^a=ef,f^a=fg,h^b=h^10,e^c=ef,f^c=fg139 conjugacy classes — view the full character table.
| maximal subgroup of | D11×#2208, C2×#13070659, #14908036, … |
| maximal normal subgroup of | D11×#2208, C2×#13070659, #14908036, … |
| maximal quotient of | #14667915, #14667919, #14667953, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 6553);