Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
| direct product | SD16×#3633 |
| Fitting | SD16×C17 ⋊ C8 |
| Sylow | C17 ⋊ C8×SD16 |
180 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 59 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 136 |
70 conjugacy classes — view the full character table.
| maximal subgroup of | C2×SD16×#3633, #135×#3633, AGL(1,ℤ/8)×#3633, … |
| maximal normal subgroup of | C2×SD16×#3633, #135×#3633, AGL(1,ℤ/8)×#3633, … |
| maximal quotient of | #102×#3633, #103×#3633, #106×#3633, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 21637);