Finite Group DatabasebetaFinite Group Databasebeta| order | 19168 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C4⋊(C599⋊C8) |
| Sylow | C599 ⋊ C4⋊C8 |
38 conjugacy classes of subgroups.
| transitive degree | μt(G) = 19168 |
Polycyclic presentation:
2^5,599|a^2=d,b^2=c,d^2=e,b^a=bc,f^a=f^5984804 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D4⋊(C599⋊C8), #50305619, Q8⋊(C599⋊C8), … |
| maximal normal subgroup of | D4⋊(C599⋊C8), #50305619, Q8⋊(C599⋊C8), … |
| maximal quotient of | #50305641, #50305643, #50305645, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19168, 76);