Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
| direct product | C2×#41×#261 |
| unambiguous semidirect product | D13⋊(C4×#41) |
| Fitting | C2×C13×#41 ⋊ C4 |
| Sylow | C13 ⋊ C2×C4×#41 |
1728 conjugacy classes of subgroups.
| transitive degree | μt(G) = 208 |
140 conjugacy classes — view the full character table.
| maximal subgroup of | #16785402, #16785405, #16785447, … |
| maximal normal subgroup of | #16785402, #16785405, #16785447, … |
| maximal quotient of | C2×#117×#261, C2×C4×D4×#261, C2×C4×Q8×#261, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 21486);