Finite Group DatabasebetaFinite Group Databasebeta| order | 2028 |
| isoclinism | isoclinic class of D39 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C13 · Schur multiplier (H2) = C1 |
| direct product | C13×Dic39 |
| unambiguous semidirect product | C3⋊(C13×Dic13) |
| derived | C3×C13 ⋊ C4×C13 |
| Hall | C3×C132 ⋊ C4 |
| Sylow | C132 ⋊ Dic3 |
| Sylow | C3 ⋊ C13×Dic13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C13 | D39 |
| commutator, hypocenter | C3×C13 | C4×C13 |
| Frattini | C2 | C13×D39 |
| Fitting, socle, prime radical | C2×C3×C132 | C2 |
| cosocle | C2×C3×C13 | C2×C13 |
| LCS | G ▷ C3×C13 | |
| UCS | C1 ◁ C2×C13 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 156 |
546 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3⋊#17990042, C7×C13×Dic39, C13×Dic273, … |
| maximal normal subgroup of | C7×C13×Dic39, C11×C13×Dic39, C13×C17×Dic39, … |
| maximal quotient of | C7×C13×Dic39, C13×Dic273, C13×Dic429, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2028, 34);