Finite Group DatabasebetaFinite Group Databasebeta| order | 16428 |
| isoclinism | isoclinic class of C3⋊#3866 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C37 · Schur multiplier (H2) = C1 |
| direct product | C37×C3⋊#3866 |
| unambiguous semidirect product | C3⋊(C37×#3866) |
| Fitting, socle, Hall | C3×C372 ⋊ C4 |
| derived | C3×C37 ⋊ C4×C37 |
| Sylow | C372 ⋊ Dic3 |
| Sylow | C3 ⋊ C37×#3866 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C37 | C3⋊#3866 |
| commutator, hypocenter | C3×C37 | C4×C37 |
| Frattini | C1 | G |
| Fitting, socle | C3×C372 | C4 |
| prime radical | C3×C37×D37 | C2 |
| cosocle | C3×D37 | C2×C37 |
| LCS | G ▷ C3×C37 | |
| UCS | C1 ◁ C37 | |
42 conjugacy classes of subgroups.
| transitive degree | μt(G) = 444 |
1221 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16428, 70);