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,h^a=h^10,c^b=cg,h^b=h^10256 conjugacy classes — view the full character table.
| maximal subgroup of | #14640741, #14640745, #14659124, … |
| maximal normal subgroup of | #14640741, #14640745, #14659124, … |
| maximal quotient of | #14643154, #14643159, #14643162, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 4208);