Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | C2×C4⋊#11764049 |
| Fitting | C2×C4×C137 ⋊ C8 |
| Sylow | C137 ⋊ C2×C4⋊C8 |
138 conjugacy classes of subgroups.
176 conjugacy classes — view the full character table.
| maximal subgroup of | #31797795, #31797797, #31797801, … |
| maximal normal subgroup of | #31797795, #31797797, #31797801, … |
| maximal quotient of | C2×#22578492, C2×#22578493, #31797913, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 1661);