Finite Group DatabasebetaFinite Group Databasebeta| order | 1053 |
| isoclinism | isoclinic class of C13⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C81 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C13⋊C81 |
| derived, Sylow | C13 ⋊ C81 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C27 | C13⋊C3 |
| commutator, hypocenter | C13 | C81 |
| Fitting, cosocle | C13×C27 | C3 |
| socle, prime radical | C3×C13 | C27 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C27 | |
10 conjugacy classes of subgroups.
| minimal degree | μ(G) = 94 |
| transitive degree | μt(G) = 1053 |
Polycyclic presentation:
3^4,13|a^3=b,b^3=c,c^3=d,e^a=e^3189 conjugacy classes — view the full character table.
| maximal subgroup of | C13⋊C3×C81, C3×C13⋊C81, #15691516, … |
| maximal normal subgroup of | C13⋊C3×C81, C3×C13⋊C81, #15691516, … |
| maximal quotient of | C13⋊C243, C3×C13⋊C81 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1053, 16);