Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | SD32×#595 |
| Fitting | C17×SD32 ⋊ C4 |
| Sylow | C17 ⋊ C4×SD32 |
162 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 162 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 | C2×SD32×#595, #508×#595, #509×#595, … |
| maximal normal subgroup of | C2×SD32×#595, #508×#595, #509×#595, … |
| maximal quotient of | SD32×#3624, #17960200, #17960201, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 20904);