Finite Group DatabasebetaFinite Group Databasebeta| order | 34461 |
| automorphism | ? |
| homology | Abelianization (H1) = C7×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C547⋊C7)⋊C9 |
| unambiguous semidirect product | (C547⋊C9)⋊C7 |
| derived, Sylow | C547 ⋊ C7×C9 |
| Hall | C547⋊C9 ⋊ C7 |
| Hall | C547⋊C7 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | (C547⋊C3)⋊C7 |
| commutator, hypocenter | C547 | C7×C9 |
| Fitting, socle, cosocle | C3×C547 | C3×C7 |
| prime radical | C3×C547⋊C7 | C3 |
| LCS | G ▷ C547 | |
| UCS | C1 ◁ C3 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4923 |
Polycyclic presentation:
3,7,547,3|a^3=d,c^a=c^40,c^b=c^81141 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34461, 2);