Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | C2×#19128775 |
| Fitting | C2×Q16×C167 ⋊ C2 |
| Sylow | C167 ⋊ C2×SD32 |
90 conjugacy classes of subgroups.
1184 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36325987, C4×#19128775, #36326000, … |
| maximal normal subgroup of | #36325987, C4×#19128775, #36326000, … |
| maximal quotient of | C2×#24923069, C2×#24923073, C2×#24923096, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 972);