Finite Group DatabasebetaFinite Group Databasebeta| order | 2028 |
| isoclinism | isoclinic class of D13⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C13 · Schur multiplier (H2) = C1 |
| direct product | C13×Dic13⋊C3 |
| unambiguous semidirect product | Dic13⋊(C3×C13) |
| derived | C13 ⋊ C3×C4×C13 |
| Hall | C13×Dic13 ⋊ C3 |
| Hall | C13×C13⋊C3 ⋊ C4 |
| Sylow | C132 ⋊ C3×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C13 | D13⋊C3 |
| commutator, hypocenter | C13 | C3×C4×C13 |
| Frattini | C2 | C13×D13⋊C3 |
| Fitting, socle | C2×C132 | C2×C3 |
| prime radical | C2×C13×C13⋊C3 | C2 |
| cosocle | C2×C13 | C2×C3×C13 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C2×C13 | |
28 conjugacy classes of subgroups.
| transitive degree | μt(G) = 156 |
208 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2028, 21);