Finite Group DatabasebetaFinite Group Databasebeta| order | 2028 |
| isoclinism | isoclinic class of D169⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | Dic169⋊C3 |
| derived, Sylow | C169 ⋊ C3×C4 |
| Hall | Dic169 ⋊ C3 |
| Hall | C169⋊C3 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D169⋊C3 |
| commutator, hypocenter | C169 | C3×C4 |
| Frattini, socle | C2×C13 | D13⋊C3 |
| Fitting, cosocle | C2×C169 | C2×C3 |
| prime radical | C2×C169⋊C3 | C2 |
| LCS | G ▷ C169 | |
| UCS | C1 ◁ C2 | |
18 conjugacy classes of subgroups.
| minimal degree | μ(G) = 173 |
| transitive degree | μt(G) = 676 |
Polycyclic presentation:
2,3,13,2,13|a^2=d,c^13=e^12,c^a=c^12e,e^a=e^12,c^b=c^3e^2,e^b=e^368 conjugacy classes — view the full character table.
| maximal subgroup of | C7×Dic169⋊C3, #28382076, #28382078, … |
| maximal normal subgroup of | C7×Dic169⋊C3, C11×Dic169⋊C3, C17×Dic169⋊C3, … |
| maximal quotient of | C7×Dic169⋊C3, #28382076, #28382078, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2028, 2);