Finite Group DatabasebetaFinite Group Databasebeta| order | 19168 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | Q16×D599 |
| Fitting | Q16×C599 ⋊ C2 |
| Sylow | C599 ⋊ C2×Q16 |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9584 |
2107 conjugacy classes. The character table is too large to display.
| maximal subgroup of | SD32×D599, Q32×D599, #50306329, … |
| maximal normal subgroup of | SD32×D599, Q32×D599, #50306329, … |
| maximal quotient of | #103×D599, #107×D599, #50305982, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19168, 162);