Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
| direct product | Q16×#3633 |
| Fitting | Q16×C17 ⋊ C8 |
| Sylow | C17 ⋊ C8×Q16 |
164 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 59 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 272 |
70 conjugacy classes — view the full character table.
| maximal subgroup of | SD32×#3633, Q32×#3633, #17982287, … |
| maximal normal subgroup of | SD32×#3633, Q32×#3633, #17982287, … |
| maximal quotient of | #103×#3633, #107×#3633, #17981698, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 21638);