Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C22×#14581939 |
| Fitting | C22×C8×C167 ⋊ C2 |
| Sylow | C167 ⋊ C22×SD16 |
298 conjugacy classes of subgroups.
2684 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36324471, #36324473, #36324492, … |
| maximal normal subgroup of | #36324471, #36324473, #36324492, … |
| maximal quotient of | C22×#19128754, C22×#19128757, C22×#19128764, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 1323);