Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4 |
| direct product | D17×H(3,ℤ/4) |
| Fitting | C17×H(3,ℤ/4) ⋊ C2 |
| Sylow | C17 ⋊ C2×H(3,ℤ/4) |
404 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 135 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 272 |
220 conjugacy classes — view the full character table.
| maximal subgroup of | D17×#1339, D17×#1340, #16944471, … |
| maximal normal subgroup of | D17×#1339, D17×#1340, #16944471, … |
| maximal quotient of | D17×#1274, #16923721, #16923724, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 4209);