Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | D8×#3633 |
| Fitting | D8×C17 ⋊ C8 |
| Sylow | C17 ⋊ C8×D8 |
196 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 196 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 | D16×#3633, SD32×#3633, #17982287, … |
| maximal normal subgroup of | D16×#3633, SD32×#3633, #17982287, … |
| maximal quotient of | #102×#3633, #107×#3633, #17981697, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 21636);