Finite Group DatabasebetaFinite Group Databasebeta| order | 19314 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C29⋊(#66526⋊C2) |
| unambiguous semidirect product | #66526⋊D29 |
| Fitting, socle, derived, Hall | C29×C37 ⋊ C2×C9 |
| Hall | C29×#66526 ⋊ C2 |
| Hall | D1073 ⋊ C9 |
| Hall | #66526 ⋊ D29 |
| Sylow | C37 ⋊ C9×D29 |
| Sylow | C29 ⋊ #66526⋊C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C29×C37 | C2×C9 |
| prime radical | C29⋊(D37⋊C3) | C3 |
| cosocle | C29×C37⋊C3 | C2×C3 |
| LCS | G ▷ C29×C37 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1073 |
Polycyclic presentation:
2,3^2,29,37|b^3=c,d^a=d^28,e^a=e^36,e^b=e^16,e^c=e^26202 conjugacy classes — view the full character table.
| maximal subgroup of | #50311192, #50311193, D29×#66526⋊C2, … |
| maximal normal subgroup of | #50311192, #50311193, D29×#66526⋊C2, … |
| maximal quotient of | #50311168, C2×C29⋊(#66526⋊C2) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19314, 15);