Finite Group DatabasebetaFinite Group Databasebeta| order | 16428 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | Dic1369⋊C3 |
| derived, Sylow | C1369 ⋊ C3×C4 |
| Hall | Dic1369 ⋊ C3 |
| Hall | C1369⋊C3 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D1369⋊C3 |
| commutator, hypocenter | C1369 | C3×C4 |
| Frattini, socle | C2×C37 | D37⋊C3 |
| Fitting, cosocle | C2×C1369 | C2×C3 |
| prime radical | C2×C1369⋊C3 | C2 |
| LCS | G ▷ C1369 | |
| UCS | C1 ◁ C2 | |
18 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5476 |
Polycyclic presentation:
2,3,37,2,37|a^2=d,c^37=e^36,c^a=c^36e,e^a=e^36,c^b=c^26e^22,e^b=e^26468 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16428, 2);