Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C2×M16×D167 |
| Fitting | C2×M16×C167 ⋊ C2 |
| Sylow | C167 ⋊ C22×M16 |
298 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 159 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1700 conjugacy classes. The character table is too large to display.
| maximal subgroup of | H(3,ℤ/4)×D167, #338×D167, #339×D167, … |
| maximal normal subgroup of | H(3,ℤ/4)×D167, #338×D167, #339×D167, … |
| maximal quotient of | C2×#97×D167, C4×M16×D167, C2×M16×Dic167, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 1307);