Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | C4×#14581937 |
| Fitting | C4×Q8×C167 ⋊ C2 |
| Sylow | C167 ⋊ C4×SD16 |
122 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 122 conjugacy classes of subgroups — too many to draw. Only its 55 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1688 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36322935, C8×#14581937, #36322948, … |
| maximal normal subgroup of | #36322935, C8×#14581937, #36322948, … |
| maximal quotient of | C8×#14581937, #36322972, #36322981, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 637);