Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C11 ⋊ #2176 |
148 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1408 |
Polycyclic presentation:
2^7,11|a^2=e,b^2=g,c^2=e,d^2=fg,f^2=g,b^a=bd,c^a=cg,d^a=df,f^a=fg,h^a=h^10,d^b=df,f^b=fg,h^b=h^10232 conjugacy classes — view the full character table.
| maximal subgroup of | #14641246, #14641248, #14665652, … |
| maximal normal subgroup of | #14641246, #14641248, #14665652, … |
| maximal quotient of | #14665520, #14665719, #14665777, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 6382);