Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C22×C11×M16 ⋊ C2 |
| Sylow | C11 ⋊ #2896 |
772 conjugacy classes of subgroups.
| transitive degree | μt(G) = 352 |
Polycyclic presentation:
2^7,11|a^2=f,d^2=g,e^2=g,b^a=be,c^a=cg,e^a=eg,h^a=h^10,e^b=eg,h^b=h^10244 conjugacy classes — view the full character table.
| maximal subgroup of | #14659234, #14659240, #14659266, … |
| maximal normal subgroup of | #14659234, #14659240, #14659266, … |
| maximal quotient of | #14720149, #14720209, #14720228, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 13030);