Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | #100×D167 |
| Fitting | #100×C167 ⋊ C2 |
| Sylow | C167 ⋊ C2×#100 |
186 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 53 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
935 conjugacy classes — view the full character table.
| maximal subgroup of | AΣL(1,𝔽16)×D167, #352×D167, #36325781, … |
| maximal normal subgroup of | AΣL(1,𝔽16)×D167, #352×D167, #36325781, … |
| maximal quotient of | #323×D167, #36322457, #36322463, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 524);