Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C11 ⋊ #1729 |
416 conjugacy classes of subgroups.
| transitive degree | μt(G) = 704 |
Polycyclic presentation:
2^7,11|a^2=e,b^2=f,e^2=g,b^a=bd,c^b=cg,h^b=h^10376 conjugacy classes — view the full character table.
| maximal subgroup of | #14640727, #14640729, #14659125, … |
| maximal normal subgroup of | #14640727, #14640729, #14659125, … |
| maximal quotient of | #14643155, #14643158, #14643161, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 4206);