Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#17984107 |
| Fitting | C2×D8×C137 ⋊ C2 |
| Sylow | C137 ⋊ C2×#135 |
266 conjugacy classes of subgroups.
980 conjugacy classes — view the full character table.
| maximal subgroup of | #31782493, #31782498, #31782535, … |
| maximal normal subgroup of | #31782493, #31782498, #31782535, … |
| maximal quotient of | C2×#22577396, C2×#22577440, C2×D8×Dic137, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 1328);