Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4 |
| direct product | C4×#10587680 |
| Sylow | C17 ⋊ C4×#131 |
572 conjugacy classes of subgroups; only the 288 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 288 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 | #17951905, #17951909, #17951914, … |
| maximal normal subgroup of | #17951905, #17951909, #17951914, … |
| maximal quotient of | C8×#10587680, #17964027, #17964094, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 21079);