Finite Group DatabasebetaFinite Group Databasebeta| order | 19168 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | Dic599⋊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^b=f^5984804 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4⋊C8×D599, C2×Dic599⋊C8, #50305912, … |
| maximal normal subgroup of | C4⋊C8×D599, C2×Dic599⋊C8, #50305912, … |
| maximal quotient of | #50305640, #50305642, #50305644, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19168, 75);