Finite Group DatabasebetaFinite Group Databasebeta| order | 34164 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | #26015660⋊C3 |
| unambiguous semidirect product | #26015661⋊C3 |
| unambiguous semidirect product | #26015666⋊C3 |
| unambiguous semidirect product | #26015677⋊C3 |
| Fitting, socle, derived, Hall | C13×C73 ⋊ C32×C4 |
| Hall | C13⋊C3×C73⋊C3 ⋊ C4 |
| Hall | #16838291 ⋊ C32 |
| Sylow | C73 ⋊ C3×AGL(1,𝔽13) |
| Sylow | C13 ⋊ C3×#64408⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C13×C73 | C32×C4 |
| prime radical | (C13⋊C3)⋊(D73⋊C3) | C2 |
| cosocle | D949 | C2×C32 |
| LCS | G ▷ C13×C73 | |
| UCS | C1 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 949 |
Polycyclic presentation:
2,3^2,2,13,73|a^2=d,e^a=e^5,f^a=f^27,f^b=f^8,e^c=e^3,e^d=e^12,f^d=f^7281 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34164, 169);