Finite Group DatabasebetaFinite Group Databasebeta| order | 1053 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C9 · Schur multiplier (H2) = C32 |
| unambiguous semidirect product | C32⋊(C13⋊C9) |
| Sylow | C13 ⋊ C32⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C32 | C3×C13⋊C3 |
| commutator | C3×C13 | C3×C9 |
| Fitting, prime radical | C33×C13 | C3 |
| socle, cosocle | C32×C13 | C32 |
| hypercenter | C33 | C13⋊C3 |
| hypocenter | C13 | C32⋊C9 |
| LCS | G ▷ C3×C13 ▷ C13 | |
| UCS | C1 ◁ C32 ◁ C33 | |
46 conjugacy classes of subgroups.
| transitive degree | μt(G) = 351 |
Polycyclic presentation:
3^4,13|a^3=d,b^a=bc,e^a=e^3141 conjugacy classes — view the full character table.
| maximal subgroup of | #15691460, #15691461, #15691462, … |
| maximal normal subgroup of | #15691460, #15691461, #15691462, … |
| maximal quotient of | C13⋊#6855, C32⋊(C13⋊C27), #15691486, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1053, 19);