Finite Group DatabasebetaFinite Group Databasebeta| order | 19168 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C42×C599 ⋊ C2 |
| Sylow | C599 ⋊ #117 |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9584 |
Polycyclic presentation:
2^5,599|a^2=e,c^2=d,b^a=bd,f^b=f^5984804 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #50305844, #50305847, #50305905, … |
| maximal normal subgroup of | #50305844, #50305847, #50305905, … |
| maximal quotient of | #50305736, C4×(C2×D599)⋊C4, C4×Dic599⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19168, 103);