Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | C2×#17984146 |
| Fitting | C24×C137 ⋊ C4 |
| Sylow | C137 ⋊ C2×#99 |
210 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 52 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
566 conjugacy classes — view the full character table.
| maximal subgroup of | #31795873, #31795874, C4×#17984146, … |
| maximal normal subgroup of | #31795873, #31795874, C4×#17984146, … |
| maximal quotient of | C2×#22578246, C2×#22578249, #31796024, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 1525);