Finite Group DatabasebetaFinite Group Databasebeta| order | 19168 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | M16×C599 ⋊ C2 |
| Sylow | C599 ⋊ #104 |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4792 |
Polycyclic presentation:
2^5,599|a^2=d,c^2=e,d^2=e,b^a=bc,c^a=ce,c^b=ce,f^b=f^5983004 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #104×D599, C2×#34062641, #50305905, … |
| maximal normal subgroup of | #104×D599, C2×#34062641, #50305905, … |
| maximal quotient of | #50305617, #50305620, #50305625, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19168, 72);