Finite Group DatabasebetaFinite Group Databasebeta| order | 19168 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C599 ⋊ #137 |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9584 |
Polycyclic presentation:
2^5,599|b^2=e,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 | #50306068, #50306069, #50306073, … |
| maximal normal subgroup of | #50306068, #50306069, #50306073, … |
| maximal quotient of | #50305891, #50305898, #50305933, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19168, 176);