Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | (C22⋊D11)⋊C16 |
| Fitting | C11×C22⋊C16 ⋊ C2 |
| Sylow | C11 ⋊ D4×C16 |
174 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 79 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=e,e^2=f,f^2=g,b^a=bd,h^c=h^10280 conjugacy classes — view the full character table.
| maximal subgroup of | D4×C16×D11, C2×(C22⋊D11)⋊C16, #14906940, … |
| maximal normal subgroup of | D4×C16×D11, C2×(C22⋊D11)⋊C16, #14906940, … |
| maximal quotient of | #14665475, #14665536, #14665542, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 6327);