Finite Group DatabasebetaFinite Group Databasebeta| order | 1053 |
| isoclinism | isoclinic class of C13⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C27 · Schur multiplier (H2) = C3 |
| direct product | C27×C13⋊C3 |
| Fitting | C13×C27 ⋊ C3 |
| derived, Sylow | C13 ⋊ C3×C27 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C27 | C13⋊C3 |
| commutator, hypocenter | C13 | C3×C27 |
| Frattini | C9 | C3×C13⋊C3 |
| Fitting | C13×C27 | C3 |
| socle | C3×C13 | C3×C9 |
| prime radical | C3×C13⋊C3 | C9 |
| cosocle | C9×C13 | C32 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C27 | |
28 conjugacy classes of subgroups.
| transitive degree | μt(G) = 351 |
189 conjugacy classes — view the full character table.
| maximal subgroup of | C13⋊C3×C81, #15691516, #15691517, … |
| maximal normal subgroup of | C13⋊C3×C81, #15691516, #15691517, … |
| maximal quotient of | C27×C13⋊C9, (C3×C13⋊C3)⋊C27, (C13⋊C9)⋊C27, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1053, 23);