Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
| direct product | C2×#19128826 |
| Fitting | C2×C42×C167 ⋊ C2 |
| Sylow | C167 ⋊ C2×#126 |
246 conjugacy classes of subgroups.
2684 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36322505, #36322508, #36326686, … |
| maximal normal subgroup of | #36322505, #36322508, #36326686, … |
| maximal quotient of | C2×#24923137, C2×#24923153, C2×#24923160, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 1074);