Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
| direct product | C2×#19128771 |
| Fitting | C2×C16×C167 ⋊ C2 |
| Sylow | C167 ⋊ C2×M32 |
90 conjugacy classes of subgroups.
2696 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36322277, C4×#19128771, #36325731, … |
| maximal normal subgroup of | #36322277, C4×#19128771, #36325731, … |
| maximal quotient of | C2×#24923044, C4×#19128771, C2×(C2×D167)⋊C16, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 963);