Finite Group DatabasebetaFinite Group Databasebeta| order | 2028 |
| isoclinism | isoclinic class of C22⋊(C169⋊C3) |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C22⋊(C169⋊C3) |
| unambiguous semidirect product | C169⋊A4 |
| Fitting, derived, Hall | C22×C169 ⋊ C3 |
| Sylow | C169 ⋊ A4 |
| Sylow | C22 ⋊ C169⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C22×C169 | C3 |
| Frattini | C13 | C22⋊(C13⋊C3) |
| socle | C22×C13 | C13⋊C3 |
| LCS | G ▷ C22×C169 | |
| UCS | C1 | |
15 conjugacy classes of subgroups.
| minimal degree | μ(G) = 173 |
| transitive degree | μt(G) = 676 |
Polycyclic presentation:
3,2^2,13^2|d^13=e^6,b^a=c,c^a=bc,d^a=d^3e,e^a=e^3228 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2028, 15);