Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C42 |
| direct product | C2×#11763745 |
| unambiguous semidirect product | D17⋊#376 |
| Fitting | C2×C42×C17 ⋊ C4 |
| Sylow | C17 ⋊ C2×#376 |
840 conjugacy classes of subgroups; only the 338 normal subgroups are shown.
This group has 840 conjugacy classes of subgroups — too many to draw. Only its 338 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 544 |
208 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#14543607, #17950314, #17950321, … |
| maximal normal subgroup of | C2×#14543607, #17950314, #17950321, … |
| maximal quotient of | C2×C4×(C2×#595)⋊C4, C4×#11763745, C2×#14543959, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 20937);