Finite Group DatabasebetaFinite Group Databasebeta| order | 19168 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C599 ⋊ C22⋊Q8 |
74 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9584 |
Polycyclic presentation:
2^5,599|a^2=d,b^2=d,b^a=bd,c^a=ce,f^a=f^5984798 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #50305626, #50305628, #50306041, … |
| maximal normal subgroup of | #50305626, #50305628, #50306041, … |
| maximal quotient of | #50305750, #50305763, #50305774, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19168, 125);