Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C4 |
| unambiguous semidirect product | C11⋊#1309 |
| Sylow | C11 ⋊ #1309 |
146 conjugacy classes of subgroups.
| transitive degree | μt(G) = 704 |
Polycyclic presentation:
2^7,11|a^2=d,b^2=e,d^2=f,e^2=g,b^a=bc,c^a=cf,e^a=eg,c^b=cg,d^b=df,h^b=h^10166 conjugacy classes — view the full character table.
| maximal subgroup of | #14641316, #14641317, #14641394, … |
| maximal normal subgroup of | #14641316, #14641317, #14641394, … |
| maximal quotient of | #14640348, #14640349, #14640369, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 2423);