Finite Group DatabasebetaFinite Group Databasebeta| order | 31740 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C23 |
| direct product | AGL(1,𝔽5)×C232⋊C3 |
| unambiguous semidirect product | (AGL(1,𝔽5)×C232)⋊C3 |
| Fitting, socle, derived, Hall | C5×C232 ⋊ C3×C4 |
| Hall | AGL(1,𝔽5)×C232 ⋊ C3 |
| Hall | C5×C232⋊C3 ⋊ C4 |
| Sylow | C232 ⋊ C3×AGL(1,𝔽5) |
| Sylow | C5 ⋊ C4×C232⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C232 | C3×C4 |
| prime radical | D5×C232⋊C3 | C2 |
| cosocle | D5×C232 | C2×C3 |
| LCS | G ▷ C5×C232 | |
| UCS | C1 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 345 |
895 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31740, 51);