Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
| direct product | C22×D17⋊M16 |
| unambiguous semidirect product | D17⋊(C22×M16) |
| Sylow | C17 ⋊ C23×M16 |
1720 conjugacy classes of subgroups; only the 810 normal subgroups are shown.
This group has 1720 conjugacy classes of subgroups — too many to draw. Only its 810 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 | #17956665, #17956673, #17956676, … |
| maximal normal subgroup of | #17956665, #17956673, #17956676, … |
| maximal quotient of | C22×#11763768, C22×C4×#63247, C2×C4×D17⋊M16, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 21496);