Finite Group DatabasebetaFinite Group Databasebeta| order | 34476 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D51⋊D169 |
| unambiguous semidirect product | D507⋊D17 |
| unambiguous semidirect product | D2873⋊D3 |
| Fitting, derived, Hall | C3×C17×C169 ⋊ C22 |
| Hall | C17×C169 ⋊ C2×D3 |
| Hall | C3×C169 ⋊ C2×D17 |
| Sylow | C169 ⋊ D3×D17 |
| Hall | C3×C17 ⋊ C2×D169 |
| Sylow | C17 ⋊ D3×D169 |
| Sylow | C3 ⋊ D17×D169 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C3×C17×C169 | C22 |
| Frattini | C13 | D39⋊D17 |
| socle | C3×C13×C17 | C2×D13 |
| LCS | G ▷ C3×C17×C169 | |
| UCS | C1 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8619 |
Polycyclic presentation:
2^2,3,13,17,13|d^13=f^12,d^a=d^12f,e^a=e^16,f^a=f^12,c^b=c^2,d^b=d^12f,f^b=f^122298 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34476, 42);