Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
| direct product | C22×#10587680 |
| Sylow | C17 ⋊ C22×#131 |
1504 conjugacy classes of subgroups; only the 770 normal subgroups are shown.
This group has 1504 conjugacy classes of subgroups — too many to draw. Only its 770 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1088 |
160 conjugacy classes — view the full character table.
| maximal subgroup of | #17956832, #17956908, #17968165, … |
| maximal normal subgroup of | #17956832, #17956908, #17968165, … |
| maximal quotient of | C22×#11763774, C2×C4×#10587680, C22×#11763784, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 21500);