Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C2×C4×C8×C11 ⋊ C2 |
| Sylow | C11 ⋊ #1923 |
292 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 109 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=f,b^2=df,c^2=d,f^2=g,b^a=bd,c^a=ce,h^a=h^10376 conjugacy classes — view the full character table.
| maximal subgroup of | D11×#1923, C2×#13069222, #14756061, … |
| maximal normal subgroup of | D11×#1923, C2×#13069222, #14756061, … |
| maximal quotient of | #14651946, #14651953, #14651960, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 5116);