Finite Group DatabasebetaFinite Group Databasebeta| order | 16428 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C4×C1369⋊C3 |
| unambiguous semidirect product | (C4×C1369)⋊C3 |
| Fitting, Hall | C4×C1369 ⋊ C3 |
| derived, Sylow | C1369 ⋊ C3×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | C1369⋊C3 |
| commutator, hypocenter | C1369 | C3×C4 |
| Frattini, socle | C2×C37 | C2×C37⋊C3 |
| Fitting | C4×C1369 | C3 |
| prime radical | C2×C1369⋊C3 | C2 |
| cosocle | C2×C1369 | C2×C3 |
| LCS | G ▷ C1369 | |
| UCS | C1 ◁ C4 | |
18 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5476 |
1836 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16428, 3);