Finite Group DatabasebetaFinite Group Databasebeta| order | 31740 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C23 · Schur multiplier (H2) = C1 |
| direct product | C23×C3⋊(C23⋊AGL(1,𝔽5)) |
| unambiguous semidirect product | C3⋊(C23×C23⋊AGL(1,𝔽5)) |
| unambiguous semidirect product | C23⋊(C23×ΓL(1,𝔽16)) |
| Fitting, socle, Hall | C3×C5×C232 ⋊ C4 |
| derived | C3×C5×C23 ⋊ C4×C23 |
| Hall | C5×C232 ⋊ Dic3 |
| Hall | C3×C232 ⋊ AGL(1,𝔽5) |
| Sylow | C232 ⋊ ΓL(1,𝔽16) |
| Hall | C3×C5 ⋊ C23×Dic23 |
| Sylow | C5 ⋊ C23×Dic69 |
| Sylow | C3 ⋊ C23×C23⋊AGL(1,𝔽5) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | C3⋊(C23⋊AGL(1,𝔽5)) |
| commutator, hypocenter | C3×C5×C23 | C4×C23 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C232 | C4 |
| prime radical | C3×D5×C232 | C2 |
| cosocle | C3×D5×C23 | C2×C23 |
| LCS | G ▷ C3×C5×C23 | |
| UCS | C1 ◁ C23 | |
136 conjugacy classes of subgroups.
| transitive degree | μt(G) = 690 |
3243 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31740, 85);