Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C11 ⋊ #2185 |
226 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 226 conjugacy classes of subgroups — too many to draw. Only its 57 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|b^2=g,d^2=fg,f^2=g,b^a=bd,c^a=ce,d^a=df,f^a=fg,d^b=df,f^b=fg,h^b=h^10139 conjugacy classes — view the full character table.
| maximal subgroup of | #14665887, #14665888, #14665898, … |
| maximal normal subgroup of | #14665887, #14665888, #14665898, … |
| maximal quotient of | #14665874, #14666218, #14666978, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 6426);