Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C11×#322 ⋊ C2 |
| Sylow | C11 ⋊ #1580 |
192 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 192 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,c^2=ef,d^2=f,e^2=g,b^a=bd,c^a=cf,d^a=df,h^a=h^10,d^b=df,h^b=h^10244 conjugacy classes — view the full character table.
| maximal subgroup of | #14665644, #14665648, #14665656, … |
| maximal normal subgroup of | #14665644, #14665648, #14665656, … |
| maximal quotient of | #14644551, #14645017, #14647701, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 3335);