Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×Q16×D137 |
| Fitting | C2×Q16×C137 ⋊ C2 |
| Sylow | C137 ⋊ C22×Q16 |
258 conjugacy classes of subgroups.
980 conjugacy classes — view the full character table.
| maximal subgroup of | #358×D137, #31782507, #362×D137, … |
| maximal normal subgroup of | #358×D137, #31782507, #362×D137, … |
| maximal quotient of | C2×#103×D137, C2×#107×D137, C4×Q16×D137, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 1324);