Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
| direct product | C2×#11719623 |
| unambiguous semidirect product | D13⋊#518 |
| Fitting | C22×D4×C13 ⋊ C4 |
| Sylow | C13 ⋊ C2×#518 |
1920 conjugacy classes of subgroups.
| transitive degree | μt(G) = 208 |
128 conjugacy classes — view the full character table.
| maximal subgroup of | #16785342, #16785344, #16785360, … |
| maximal normal subgroup of | #16785342, #16785344, #16785360, … |
| maximal quotient of | C2×#13131272, C2×#13131274, C2×#13131275, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 21487);