Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#19128830 |
| Sylow | C167 ⋊ C2×C4⋊Q8 |
290 conjugacy classes of subgroups.
1688 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36324528, #36324529, #36324531, … |
| maximal normal subgroup of | #36324528, #36324529, #36324531, … |
| maximal quotient of | C2×#24923138, C2×#24923164, C2×#24923174, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 1091);