Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C25 |
| direct product | D17×#342 |
| Fitting | C17×#342 ⋊ C2 |
| Sylow | C17 ⋊ C2×#342 |
680 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 680 conjugacy classes of subgroups — too many to draw. Only its 145 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×#1343, D17×#1344, #16944502, … |
| maximal normal subgroup of | D17×#1343, D17×#1344, #16944502, … |
| maximal quotient of | D17×#1280, #16923916, #16923922, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 4238);