Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C11×#443 ⋊ C2 |
| Sylow | C11 ⋊ #2955 |
456 conjugacy classes of subgroups.
| transitive degree | μt(G) = 352 |
Polycyclic presentation:
2^7,11|a^2=f,c^2=f,e^2=g,f^2=g,b^a=be,d^a=dg,e^a=eg,e^b=eg,h^d=h^10184 conjugacy classes — view the full character table.
| maximal subgroup of | #14907009, #14907011, #14907016, … |
| maximal normal subgroup of | #14907009, #14907011, #14907016, … |
| maximal quotient of | C8×#66964, C8×#66967, C8×#66968, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 13408);