Finite Group DatabasebetaFinite Group Databasebeta| order | 2144 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | Q16×D67 |
| Fitting | Q16×C67 ⋊ C2 |
| Sylow | C67 ⋊ C2×Q16 |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1072 |
245 conjugacy classes — view the full character table.
| maximal subgroup of | SD32×D67, Q32×D67, #16863835, … |
| maximal normal subgroup of | SD32×D67, Q32×D67, #16863835, … |
| maximal quotient of | #103×D67, #107×D67, #16863488, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2144, 162);