Finite Group DatabasebetaFinite Group Databasebeta| order | 31740 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | C3⋊(C23⋊(C23⋊AGL(1,𝔽5))) |
| unambiguous semidirect product | C23⋊(C3⋊(C23⋊AGL(1,𝔽5))) |
| Fitting, socle, derived, Hall | C3×C5×C232 ⋊ C4 |
| Hall | C5×C232 ⋊ Dic3 |
| Hall | C3×C232 ⋊ AGL(1,𝔽5) |
| Sylow | C232 ⋊ ΓL(1,𝔽16) |
| Hall | C3×C5 ⋊ C23⋊Dic23 |
| Sylow | C5 ⋊ C3⋊(C23⋊Dic23) |
| Sylow | C3 ⋊ C23⋊(C23⋊AGL(1,𝔽5)) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C5×C232 | C4 |
| prime radical, cosocle | C3×D5×C232 | C2 |
| LCS | G ▷ C3×C5×C232 | |
| UCS | C1 | |
312 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7935 |
Polycyclic presentation:
2^2,3,5,23^2|a^2=b,c^a=c^2,d^a=d^2,e^a=e^22,f^a=f^22,d^b=d^43177 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31740, 86);