Finite Group DatabasebetaFinite Group Databasebeta| order | 19266 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C13 |
| unambiguous semidirect product | C3⋊(C13⋊D247) |
| unambiguous semidirect product | C13⋊D741 |
| unambiguous semidirect product | C19⋊(C3⋊(C13⋊D13)) |
| Fitting, socle, derived, Hall | C3×C132×C19 ⋊ C2 |
| Hall | C132×C19 ⋊ D3 |
| Hall | C3×C132 ⋊ D19 |
| Sylow | C132 ⋊ D57 |
| Hall | C3×C19 ⋊ C13⋊D13 |
| Sylow | C19 ⋊ C3⋊(C13⋊D13) |
| Sylow | C3 ⋊ C13⋊D247 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C132×C19 | C2 |
| LCS | G ▷ C3×C132×C19 | |
| UCS | C1 | |
128 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9633 |
Polycyclic presentation:
2,3,13^2,19|b^a=b^2,c^a=c^12,d^a=d^12,e^a=e^184818 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D13×D741, D39×D247, D19×C3⋊(C13⋊D13), … |
| maximal normal subgroup of | D13×D741, D39×D247, D19×C3⋊(C13⋊D13), … |
| maximal quotient of | C3⋊(C19⋊#10621725), C2×C3⋊(C13⋊D247) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19266, 90);