Finite Group DatabasebetaFinite Group Databasebeta| order | 34476 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C13 |
| unambiguous semidirect product | D51⋊(C13⋊D13) |
| Fitting, socle, derived, Hall | C3×C132×C17 ⋊ C22 |
| Hall | C132×C17 ⋊ C2×D3 |
| Hall | C3×C132 ⋊ C2×D17 |
| Sylow | C132 ⋊ D3×D17 |
| Hall | C3×C17 ⋊ C2×C13⋊D13 |
| Sylow | C17 ⋊ D3×C13⋊D13 |
| Sylow | C3 ⋊ D17×C13⋊D13 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C132×C17 | C22 |
| LCS | G ▷ C3×C132×C17 | |
| UCS | C1 | |
320 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8619 |
Polycyclic presentation:
2^2,3,13^2,17|d^a=d^12,e^a=e^12,f^a=f^16,c^b=c^2,d^b=d^12,e^b=e^122298 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34476, 247);