Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C11×#334 ⋊ C2 |
| Sylow | C11 ⋊ C8×SD16 |
180 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 73 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,d^2=f,e^2=g,b^a=bd,d^a=df,d^b=df,h^b=h^10,h^c=h^10196 conjugacy classes — view the full character table.
| maximal subgroup of | C8×SD16×D11, C2×#13067415, C8×#66969, … |
| maximal normal subgroup of | C8×SD16×D11, C2×#13067415, C8×#66969, … |
| maximal quotient of | #14644534, #14644541, #14645000, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 3309);