Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C11×#417 ⋊ 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,e^b=eg,h^c=h^10,h^d=h^10154 conjugacy classes — view the full character table.
| maximal subgroup of | #14753066, #14753068, #14753073, … |
| maximal normal subgroup of | #14753066, #14753068, #14753073, … |
| maximal quotient of | #14720145, #14720205, #14720224, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 13026);