Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C22×D1336 |
| Fitting | C22×C8×C167 ⋊ C2 |
| Sylow | C167 ⋊ C22×D8 |
338 conjugacy classes of subgroups.
2684 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36324485, #36324487, #36325002, … |
| maximal normal subgroup of | #36324485, #36324487, #36325002, … |
| maximal quotient of | C22×#19128754, C22×#19128766, C2×C4×D1336, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 1319);