Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C25 |
| direct product | C2×(C2×#10587739)⋊C4 |
| unambiguous semidirect product | D137⋊#95 |
| Fitting | C22×C4×C137 ⋊ C4 |
| Sylow | C137 ⋊ C2×#95 |
330 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 124 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 | #31795626, #31795662, #31795664, … |
| maximal normal subgroup of | #31795626, #31795662, #31795664, … |
| maximal quotient of | C4×(C2×#10587739)⋊C4, #31795962, #31795963, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 1484);