Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | D16×#595 |
| Fitting | C17×D16 ⋊ C4 |
| Sylow | C17 ⋊ C4×D16 |
174 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 50 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 272 |
88 conjugacy classes — view the full character table.
| maximal subgroup of | D32×#595, SD64×#595, #17962878, … |
| maximal normal subgroup of | D32×#595, SD64×#595, #17962878, … |
| maximal quotient of | D16×#3624, #17960197, #17960198, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 20903);