Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C11×#416 ⋊ C2 |
| Sylow | C11 ⋊ #2898 |
726 conjugacy classes of subgroups.
| transitive degree | μt(G) = 704 |
Polycyclic presentation:
2^7,11|a^2=f,b^2=g,e^2=g,b^a=be,e^a=eg,e^b=eg,d^c=dg,h^c=h^10,h^d=h^10184 conjugacy classes — view the full character table.
| maximal subgroup of | #14769762, #14769771, #14769777, … |
| maximal normal subgroup of | #14769762, #14769771, #14769777, … |
| maximal quotient of | #14720158, #14720256, #14720264, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 13039);