Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C2×D137⋊M16 |
| unambiguous semidirect product | D137⋊(C2×M16) |
| Sylow | C137 ⋊ C22×M16 |
298 conjugacy classes of subgroups; only the 148 normal subgroups are shown.
This group has 298 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 | #31796451, #31796454, C2×#22578270, … |
| maximal normal subgroup of | #31796451, #31796454, C2×#22578270, … |
| maximal quotient of | C2×#22578362, C2×C4×#14555519, C4×D137⋊M16, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 1622);