Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C11×#436 ⋊ C2 |
| Sylow | C11 ⋊ D4×M16 |
544 conjugacy classes of subgroups.
| transitive degree | μt(G) = 352 |
Polycyclic presentation:
2^7,11|a^2=f,c^2=f,f^2=g,b^a=be,d^a=dg,h^b=h^10,d^c=dg,h^c=h^10,h^d=h^10190 conjugacy classes — view the full character table.
| maximal subgroup of | #14724657, #14724663, #14724668, … |
| maximal normal subgroup of | #14724657, #14724663, #14724668, … |
| maximal quotient of | #14725195, #14725203, #14725212, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 13246);