Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C11×#407 ⋊ C2 |
| Sylow | C11 ⋊ #1783 |
820 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 820 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) = 176 |
Polycyclic presentation:
2^7,11|a^2=f,f^2=g,b^a=bd,c^a=ce,d^a=dg,f^b=fg,h^b=h^10172 conjugacy classes — view the full character table.
| maximal subgroup of | #14641123, #14641127, #14645899, … |
| maximal normal subgroup of | #14641123, #14641127, #14645899, … |
| maximal quotient of | #14645099, #14645113, #14645123, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 4430);