Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4 |
| direct product | C2×#17984167 |
| unambiguous semidirect product | D137⋊#117 |
| Fitting | C22×C4×C137 ⋊ C4 |
| Sylow | C137 ⋊ C2×#117 |
330 conjugacy classes of subgroups; only the 148 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 148 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
584 conjugacy classes — view the full character table.
| maximal subgroup of | #31796454, #31796457, C2×#22578270, … |
| maximal normal subgroup of | #31796454, #31796457, C2×#22578270, … |
| maximal quotient of | C2×#22578339, C2×C4×C22⋊#10587739, C2×C4×C4⋊#10587739, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 1612);