Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C4×#66969 |
| Fitting | C4×C11×SD16 ⋊ C2 |
| Sylow | C11 ⋊ C4×#135 |
500 conjugacy classes of subgroups.
| transitive degree | μt(G) = 704 |
196 conjugacy classes — view the full character table.
| maximal subgroup of | C8×#66969, #14723174, #14723251, … |
| maximal normal subgroup of | C8×#66969, #14723174, #14723251, … |
| maximal quotient of | C8×#66969, #14723299, #14723301, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 13279);