Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
| direct product | C2×#11763877 |
| unambiguous semidirect product | D17⋊#519 |
| Fitting | C22×Q8×C17 ⋊ C4 |
| Sylow | C17 ⋊ C2×#519 |
1488 conjugacy classes of subgroups; only the 762 normal subgroups are shown.
This group has 1488 conjugacy classes of subgroups — too many to draw. Only its 762 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 544 |
148 conjugacy classes — view the full character table.
| maximal subgroup of | #17956750, #17956752, #17956780, … |
| maximal normal subgroup of | #17956750, #17956752, #17956780, … |
| maximal quotient of | C2×#14545222, C2×#14545224, C4×#11763877, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 21488);