Finite Group DatabasebetaFinite Group Databasebeta| order | 31740 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5×C23 · Schur multiplier (H2) = C1 |
| direct product | C5×C23×Dic69 |
| unambiguous semidirect product | C3⋊(C5×C23×Dic23) |
| unambiguous semidirect product | C23⋊(C5×Dic3×C23) |
| derived | C3×C23 ⋊ C4×C5×C23 |
| Hall | C3×C5×C232 ⋊ C4 |
| Hall | C5×C232 ⋊ Dic3 |
| Hall | C3×C232 ⋊ C4×C5 |
| Sylow | C232 ⋊ C5×Dic3 |
| Hall | C3×C5 ⋊ C23×Dic23 |
| Sylow | C3 ⋊ C5×C23×Dic23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5×C23 | D69 |
| commutator, hypocenter | C3×C23 | C4×C5×C23 |
| Frattini | C2 | C5×C23×D69 |
| Fitting, socle, prime radical | C2×C3×C5×C232 | C2 |
| cosocle | C2×C3×C23 | C2×C5×C23 |
| LCS | G ▷ C3×C23 | |
| UCS | C1 ◁ C2×C5×C23 | |
136 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1380 |
8280 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31740, 40);