Finite Group DatabasebetaFinite Group Databasebeta| order | 1053 |
| isoclinism | isoclinic class of #66848 |
| automorphism | ? |
| homology | Abelianization (H1) = C33 · Schur multiplier (H2) = C34 |
| direct product | C3×C32⋊(C13⋊C3) |
| unambiguous semidirect product | (C3×C13)⋊H(3,𝔽3) |
| Fitting | C33×C13 ⋊ C3 |
| Sylow | C13 ⋊ C3×H(3,𝔽3) |
| subgroup | G/H | |
|---|---|---|
| center | C32 | C3×C13⋊C3 |
| commutator, cosocle | C3×C13 | C33 |
| Frattini | C3 | C32×C13⋊C3 |
| Fitting | C33×C13 | C3 |
| socle | C32×C13 | C32 |
| hypercenter | C33 | C13⋊C3 |
| hypocenter | C13 | C3×H(3,𝔽3) |
| LCS | G ▷ C3×C13 ▷ C13 | |
| UCS | C1 ◁ C32 ◁ C33 | |
112 conjugacy classes of subgroups.
| transitive degree | μt(G) = 351 |
141 conjugacy classes — view the full character table.
| maximal subgroup of | #15691460, #15691461, #15691462, … |
| maximal normal subgroup of | #15691460, #15691461, #15691462, … |
| maximal quotient of | C3×(C3×C13⋊C3)⋊C9, C3×C32⋊(C13⋊C9), C9×C32⋊(C13⋊C3), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1053, 41);