Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | SD16×Dic167 |
| Sylow | C167 ⋊ C4×SD16 |
122 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 122 conjugacy classes of subgroups — too many to draw. Only its 59 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1190 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×SD16×D167, C2×SD16×Dic167, C4×#19128853, … |
| maximal normal subgroup of | C4×SD16×D167, C2×SD16×Dic167, C4×#19128853, … |
| maximal quotient of | SD16×C167⋊C8, #36322975, #36322982, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 638);