Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
| direct product | C2×#11763731 |
| Sylow | C17 ⋊ C2×#364 |
168 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 90 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 544 |
184 conjugacy classes — view the full character table.
| maximal subgroup of | #17948556, #17948557, #17948559, … |
| maximal normal subgroup of | #17948556, #17948557, #17948559, … |
| maximal quotient of | C2×#14543806, #17960055, C2×#14543813, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 20848);