Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×#11719083 |
| unambiguous semidirect product | D13⋊#389 |
| Fitting | C2×C13×C4⋊C4 ⋊ C4 |
| Sylow | C13 ⋊ C2×#389 |
800 conjugacy classes of subgroups.
| transitive degree | μt(G) = 416 |
116 conjugacy classes — view the full character table.
| maximal subgroup of | #16785771, #16785773, #16785781, … |
| maximal normal subgroup of | #16785771, #16785773, #16785781, … |
| maximal quotient of | C2×#13130013, C2×#13130016, C4×#11719083, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 20965);