Finite Group DatabasebetaFinite Group Databasebeta| order | 20820 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D15⋊D347 |
| unambiguous semidirect product | D1041⋊D5 |
| unambiguous semidirect product | D1735⋊D3 |
| Fitting, socle, derived, Hall | C3×C5×C347 ⋊ C22 |
| Hall | C5×C347 ⋊ C2×D3 |
| Hall | C3×C347 ⋊ C2×D5 |
| Sylow | C347 ⋊ D3×D5 |
| Hall | C3×C5 ⋊ C2×D347 |
| Sylow | C5 ⋊ D3×D347 |
| Sylow | C3 ⋊ D5×D347 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C5×C347 | C22 |
| LCS | G ▷ C3×C5×C347 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5205 |
Polycyclic presentation:
2^2,3,5,347|d^a=d^4,e^a=e^346,c^b=c^2,d^b=d^41569 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20820, 20);