Finite Group DatabasebetaFinite Group Databasebeta| order | 34476 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊#26040085 |
| Fitting, derived, Hall | C3×C17×C169 ⋊ C4 |
| Hall | C17×C169 ⋊ Dic3 |
| Hall | C3×C169 ⋊ #595 |
| Sylow | C169 ⋊ C3⋊#595 |
| Hall | C3×C17 ⋊ Dic169 |
| Sylow | C17 ⋊ Dic507 |
| Sylow | C3 ⋊ #26040085 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C3×C17×C169 | C4 |
| Frattini | C13 | C3⋊#11725133 |
| socle | C3×C13×C17 | Dic13 |
| prime radical | C3×C13×D17 | D13 |
| cosocle | C3×D17×C169 | C2 |
| LCS | G ▷ C3×C17×C169 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8619 |
Polycyclic presentation:
2^2,3,13,17,13|a^2=b,d^13=f^12,c^a=c^2,d^a=d^12f,e^a=e^13,f^a=f^12,e^b=e^162538 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34476, 37);