Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
| direct product | Q16×#1057 |
| Sylow | C13 ⋊ C8×Q16 |
164 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 74 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1664 |
98 conjugacy classes — view the full character table.
| maximal subgroup of | SD32×#1057, #16788796, Q32×#1057, … |
| maximal normal subgroup of | SD32×#1057, #16788796, Q32×#1057, … |
| maximal quotient of | #103×#1057, #107×#1057, #16782501, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 20096);