Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C26 |
| direct product | C2×#11719047 |
| Sylow | C13 ⋊ C22×#97 |
680 conjugacy classes of subgroups; only the 338 normal subgroups are shown.
This group has 680 conjugacy classes of subgroups — too many to draw. Only its 338 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 832 |
176 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#13129661, #16778937, #16778944, … |
| maximal normal subgroup of | C2×#13129661, #16778937, #16778944, … |
| maximal quotient of | C2×#13130032, #16792598, C2×#13130044, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 21063);