Finite Group DatabasebetaFinite Group Databasebeta| order | 2028 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C169 · Schur multiplier (H2) = C2 |
| direct product | C2×D3×C169 |
| unambiguous semidirect product | C3⋊(C22×C169) |
| unambiguous semidirect product | (C2×C3)⋊(C2×C169) |
| Fitting | C2×C3×C169 ⋊ C2 |
| derived, Sylow | C3 ⋊ C22×C169 |
| Hall | C3×C169 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C169 | D3 |
| commutator, hypocenter | C3 | C22×C169 |
| Frattini | C13 | C2×D3×C13 |
| Fitting | C2×C3×C169 | C2 |
| socle | C2×C3×C13 | C2×C13 |
| prime radical | C2×D3×C13 | C13 |
| cosocle | C3×C13 | C22×C13 |
| LCS | G ▷ C3 | |
| UCS | C1 ◁ C2×C169 | |
30 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1014 |
1014 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×D7×C169, C2×D3×C7×C169, C2×D21×C169, … |
| maximal normal subgroup of | C2×D3×C7×C169, C2×D3×C11×C169, C2×D3×C17×C169, … |
| maximal quotient of | D3×D7×C169, C2×D3×C7×C169, C2×D21×C169, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2028, 17);