Finite Group DatabasebetaFinite Group Databasebeta| order | 19168 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | SD16×D599 |
| Fitting | SD16×C599 ⋊ C2 |
| Sylow | C599 ⋊ C2×SD16 |
68 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4792 |
2107 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×SD16×D599, #135×D599, AGL(1,ℤ/8)×D599, … |
| maximal normal subgroup of | C2×SD16×D599, #135×D599, AGL(1,ℤ/8)×D599, … |
| maximal quotient of | #102×D599, #103×D599, #106×D599, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19168, 158);