Finite Group DatabasebetaFinite Group Databasebeta| order | 34404 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D141⋊D61 |
| unambiguous semidirect product | D183⋊D47 |
| unambiguous semidirect product | D2867⋊D3 |
| Fitting, socle, derived, Hall | C3×C47×C61 ⋊ C22 |
| Hall | C47×C61 ⋊ C2×D3 |
| Hall | C3×C61 ⋊ C2×D47 |
| Hall | C3×C47 ⋊ C2×D61 |
| Sylow | C61 ⋊ D3×D47 |
| Sylow | C47 ⋊ D3×D61 |
| Sylow | C3 ⋊ D47×D61 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C47×C61 | C22 |
| LCS | G ▷ C3×C47×C61 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8601 |
Polycyclic presentation:
2^2,3,47,61|d^a=d^46,e^a=e^60,c^b=c^2,d^b=d^462235 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34404, 30);