Finite Group DatabasebetaFinite Group Databasebeta| order | 33462 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(C11⋊((C13⋊C3)⋊D13)) |
| unambiguous semidirect product | C11⋊(C3⋊((C13⋊C3)⋊D13)) |
| unambiguous semidirect product | (C13⋊C3)⋊D429 |
| Fitting, socle, derived | C3×C11×C132 ⋊ C2×C3 |
| Hall | C3×C11×C13×C13⋊C3 ⋊ C2 |
| Hall | C11×C132 ⋊ C3×D3 |
| Hall | C3×C13×C13⋊C3 ⋊ D11 |
| Sylow | C132 ⋊ C3×D33 |
| Sylow | C11 ⋊ C3⋊((C13⋊C3)⋊D13) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C11×C132 | C2×C3 |
| LCS | G ▷ C3×C11×C132 | |
| UCS | C1 | |
104 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1287 |
Polycyclic presentation:
2,3^2,11,13^2|c^a=c^2,d^a=d^10,e^a=e^12,f^a=f^12,e^b=e^31506 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33462, 109);