Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4 |
| direct product | C2×#11719071 |
| unambiguous semidirect product | D13⋊#388 |
| Fitting | C2×C13×C22⋊C4 ⋊ C4 |
| Sylow | C13 ⋊ C2×#388 |
928 conjugacy classes of subgroups.
| transitive degree | μt(G) = 416 |
116 conjugacy classes — view the full character table.
| maximal subgroup of | #16780378, C4×#11719071, #261×#388, … |
| maximal normal subgroup of | #16780378, C4×#11719071, #261×#388, … |
| maximal quotient of | C2×#13130011, C2×#13130016, C2×#13130017, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 20963);