Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×#19128756 |
| Sylow | C167 ⋊ C2×#103 |
162 conjugacy classes of subgroups.
1688 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×#19128756, #103×Dic167, #36323968, … |
| maximal normal subgroup of | C4×#19128756, #103×Dic167, #36323968, … |
| maximal quotient of | C2×Q8⋊(C167⋊C8), #36322541, #36322567, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 540);