Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | Q32×#595 |
| Fitting | C17×Q32 ⋊ C4 |
| Sylow | C17 ⋊ C4×Q32 |
150 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 150 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) = 544 |
88 conjugacy classes — view the full character table.
| maximal subgroup of | SD64×#595, Q64×#595, #17962878, … |
| maximal normal subgroup of | SD64×#595, Q64×#595, #17962878, … |
| maximal quotient of | Q32×#3624, #17960204, #17960205, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 20905);