Finite Group DatabasebetaFinite Group Databasebeta| order | 20940 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊#20296121 |
| Fitting, socle, derived, Hall | C3×C5×C349 ⋊ C4 |
| Hall | C5×C349 ⋊ Dic3 |
| Hall | C3×C349 ⋊ AGL(1,𝔽5) |
| Sylow | C349 ⋊ ΓL(1,𝔽16) |
| Hall | C3×C5 ⋊ #13063703 |
| Sylow | C5 ⋊ C3⋊#13063703 |
| Sylow | C3 ⋊ #20296121 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C5×C349 | C4 |
| prime radical, cosocle | C3×D1745 | C2 |
| LCS | G ▷ C3×C5×C349 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5235 |
Polycyclic presentation:
2^2,3,5,349|a^2=b,c^a=c^2,d^a=d^2,e^a=e^136,d^b=d^4,e^b=e^3481314 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20940, 34);