Finite Group DatabasebetaFinite Group Databasebeta| order | 34476 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #11759813⋊D17 |
| Fitting, socle, Hall | C132×C17 ⋊ C2×D3 |
| derived, Hall | C17×#92789 ⋊ C22 |
| Hall | #92789 ⋊ C2×D17 |
| Sylow | C132 ⋊ D3×D17 |
| Sylow | C17 ⋊ #11759813⋊C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C17×#92789 | C22 |
| Fitting, socle | C132×C17 | C2×D3 |
| LCS | G ▷ C17×#92789 | |
| UCS | C1 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 442 |
Polycyclic presentation:
2^2,3,17,13^2|c^a=c^2,d^a=d^16,e^a=e^9f^2,f^a=e^12f^4,c^b=c^2,e^b=e^4f^11,f^b=ef^9,e^c=e^3f^11,f^c=f^9430 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34476, 94);