Finite Group DatabasebetaFinite Group Databasebeta| order | 13053 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C19 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C229⋊C3)⋊C19 |
| unambiguous semidirect product | (C229⋊C19)⋊C3 |
| Fitting, socle, derived, Sylow | C229 ⋊ C3×C19 |
| Hall | C229⋊C19 ⋊ C3 |
| Hall | C229⋊C3 ⋊ C19 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C229 | C3×C19 |
| LCS | G ▷ C229 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
3,19,229|c^a=c^134,c^b=c^16561 conjugacy classes — view the full character table.
| maximal subgroup of | C2×(C229⋊C3)⋊C19, (D229⋊C3)⋊C19 |
| maximal normal subgroup of | C2×(C229⋊C3)⋊C19, (D229⋊C3)⋊C19 |
| maximal quotient of | C2×(C229⋊C3)⋊C19 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13053, 1);