Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C11×#367 ⋊ C2 |
| Sylow | C11 ⋊ #2177 |
172 conjugacy classes of subgroups.
| transitive degree | μt(G) = 704 |
Polycyclic presentation:
2^7,11|a^2=e,c^2=eg,d^2=fg,f^2=g,b^a=bd,c^a=cg,d^a=df,f^a=fg,d^b=df,f^b=fg,h^b=h^10,h^c=h^10142 conjugacy classes — view the full character table.
| maximal subgroup of | #14674395, #14674397, D11×#2177, … |
| maximal normal subgroup of | #14674395, #14674397, D11×#2177, … |
| maximal quotient of | #14665523, #14665695, #14665780, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 6385);