Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×#11763735 |
| unambiguous semidirect product | D17⋊#366 |
| Fitting | C2×C16×C17 ⋊ C4 |
| Sylow | C17 ⋊ C2×#366 |
168 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 74 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 544 |
172 conjugacy classes — view the full character table.
| maximal subgroup of | #17949410, #17949411, #17949428, … |
| maximal normal subgroup of | #17949410, #17949411, #17949428, … |
| maximal quotient of | C2×#14543815, #17960088, C2×#14543816, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 20859);