Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | C4×#14581940 |
| Sylow | C167 ⋊ C4×Q16 |
110 conjugacy classes of subgroups.
1688 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36322942, C8×#14581940, #36322954, … |
| maximal normal subgroup of | #36322942, C8×#14581940, #36322954, … |
| maximal quotient of | C8×#14581940, #36322986, #36322988, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 642);