Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C23 |
| direct product | D4×AGL(1,𝔽17) |
| Fitting | D4×C17 ⋊ C16 |
| Sylow | C17 ⋊ D4×C16 |
174 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 64 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 68 |
85 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 21799);