Finite Group DatabasebetaFinite Group Databasebeta| order | 19308 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #20264457⋊C3 |
| Fitting, socle, derived, Sylow | C1609 ⋊ C3×C4 |
| Hall | #20264457 ⋊ C3 |
| Hall | C1609⋊C3 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C1609 | C3×C4 |
| prime radical | D1609⋊C3 | C2 |
| cosocle | D1609 | C2×C3 |
| LCS | G ▷ C1609 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1609 |
Polycyclic presentation:
2,3,2,1609|a^2=c,d^a=d^1086,d^b=d^250,d^c=d^1608146 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19308, 8);