Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
| direct product | C2×C13⋊#564 |
| unambiguous semidirect product | (C2×C13)⋊#564 |
| Sylow | C13 ⋊ C2×#564 |
896 conjugacy classes of subgroups; only the 469 normal subgroups are shown.
This group has 896 conjugacy classes of subgroups — too many to draw. Only its 469 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1664 |
206 conjugacy classes — view the full character table.
| maximal subgroup of | #15755373, #15755374, C2×#13114137, … |
| maximal normal subgroup of | #15755373, #15755374, C2×#13114137, … |
| maximal quotient of | C2×#13118018, C2×#13118019, C2×#13118020, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 18653);