Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | D13×#456 |
| Fitting | C13×#456 ⋊ C2 |
| Sylow | C13 ⋊ C2×#456 |
708 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 708 conjugacy classes of subgroups — too many to draw. Only its 135 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 208 |
128 conjugacy classes — view the full character table.
| maximal subgroup of | D13×#1405, #15783188, D13×#2203, … |
| maximal normal subgroup of | D13×#1405, #15783188, D13×#2203, … |
| maximal quotient of | D13×#1603, D13×#1609, D13×#1604, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 13849);