Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | C2×#19128753 |
| Sylow | C167 ⋊ C2×#102 |
202 conjugacy classes of subgroups.
1688 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×#19128753, #102×Dic167, #36323963, … |
| maximal normal subgroup of | C4×#19128753, #102×Dic167, #36323963, … |
| maximal quotient of | C2×D4⋊(C167⋊C8), #36322537, #36322563, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 536);