Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C11×#416 ⋊ C2 |
| Sylow | C11 ⋊ C4×#135 |
500 conjugacy classes of subgroups.
| transitive degree | μt(G) = 704 |
Polycyclic presentation:
2^7,11|a^2=f,c^2=f,d^2=g,e^2=g,b^a=be,e^a=eg,e^b=eg,h^c=h^10196 conjugacy classes — view the full character table.
| maximal subgroup of | #14752324, #14752343, #14752362, … |
| maximal normal subgroup of | #14752324, #14752343, #14752362, … |
| maximal quotient of | #14723147, #14723298, #14723307, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 13278);