Finite Group DatabasebetaFinite Group Databasebeta| order | 2028 |
| isoclinism | isoclinic class of D169⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C2×D169⋊C3 |
| unambiguous semidirect product | D169⋊(C2×C3) |
| unambiguous semidirect product | (C169⋊C3)⋊C22 |
| unambiguous semidirect product | (C2×D169)⋊C3 |
| unambiguous semidirect product | (C2×C169⋊C3)⋊C2 |
| Fitting | C2×C169 ⋊ C2×C3 |
| derived, Sylow | C169 ⋊ C22×C3 |
| Hall | C2×D169 ⋊ C3 |
| Hall | C169⋊C3 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D169⋊C3 |
| commutator, cosocle, hypocenter | C169 | C22×C3 |
| Frattini | C13 | C2×D13⋊C3 |
| Fitting | C2×C169 | C2×C3 |
| socle | C2×C13 | D13⋊C3 |
| LCS | G ▷ C169 | |
| UCS | C1 ◁ C2 | |
30 conjugacy classes of subgroups.
| transitive degree | μt(G) = 338 |
68 conjugacy classes — view the full character table.
| maximal subgroup of | D7×D169⋊C3, #20296859⋊C2, #20296858⋊C2, … |
| maximal normal subgroup of | C2×C7×D169⋊C3, C2×C11×D169⋊C3, C2×C17×D169⋊C3, … |
| maximal quotient of | D7×D169⋊C3, #20296859⋊C2, #20296858⋊C2, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2028, 9);