Finite Group DatabasebetaFinite Group Databasebeta| order | 19168 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | #41×C599 ⋊ C2 |
| Sylow | C599 ⋊ AGL(1,ℤ/8) |
68 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4792 |
Polycyclic presentation:
2^5,599|d^2=e,b^a=bd,c^a=ce,d^a=de,d^b=de,f^b=f^5983001 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #50306058, #50306059, #50306063, … |
| maximal normal subgroup of | #50306058, #50306059, #50306063, … |
| maximal quotient of | #50305891, #50305894, #50305933, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19168, 171);