Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×#11718787 |
| Fitting | C22×C13×M16 ⋊ C2 |
| Sylow | C13 ⋊ C2×#407 |
1008 conjugacy classes of subgroups; only the 285 normal subgroups are shown.
This group has 1008 conjugacy classes of subgroups — too many to draw. Only its 285 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 416 |
296 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #15768149, #15768156, #15768159, … |
| maximal normal subgroup of | #15768149, #15768156, #15768159, … |
| maximal quotient of | C2×#13113162, C2×#13113165, C2×#13113168, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 12945);