Finite Group DatabasebetaFinite Group Databasebeta| order | 34476 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #26040084⋊C3 |
| Fitting, derived, Hall | C17×C169 ⋊ C3×C4 |
| Hall | #26040084 ⋊ C3 |
| Hall | C17×C169⋊C3 ⋊ C4 |
| Hall | C169⋊C3 ⋊ Dic17 |
| Sylow | C169 ⋊ C3×Dic17 |
| Sylow | C17 ⋊ #10621721⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C17×C169 | C3×C4 |
| Frattini | C13 | #11725132⋊C3 |
| socle | C13×C17 | AGL(1,𝔽13) |
| prime radical | C17×D169⋊C3 | C2 |
| cosocle | C17×D169 | C2×C3 |
| LCS | G ▷ C17×C169 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2873 |
Polycyclic presentation:
2,3,2,13,17,13|a^2=c,d^13=f^8,d^a=d^5f,e^a=e^16,f^a=f^5,d^b=d^3f^10,f^b=f^3,d^c=d^12f^5,f^c=f^12298 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34476, 17);