Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
| direct product | C2×#19128820 |
| Fitting | C2×C42×C167 ⋊ C2 |
| Sylow | C167 ⋊ C2×#124 |
330 conjugacy classes of subgroups.
2684 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36322489, #36322491, C2×#24923008, … |
| maximal normal subgroup of | #36322489, #36322491, C2×#24923008, … |
| maximal quotient of | C2×#24923135, C2×#24923160, C2×#24923171, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 1066);