Finite Group DatabasebetaFinite Group Databasebeta| order | 1088 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#10587600 |
| Fitting | C2×SD16×C17 ⋊ C2 |
| Sylow | C17 ⋊ C2×AGL(1,ℤ/8) |
298 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 103 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 272 |
134 conjugacy classes — view the full character table.
| maximal subgroup of | #14537589, C4×#10587600, #14537611, … |
| maximal normal subgroup of | #14537589, C4×#10587600, #14537611, … |
| maximal quotient of | C2×#11762812, C2×#11762809, C2×#11762848, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1088, 1337);