Finite Group DatabasebetaFinite Group Databasebeta| order | 31740 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | C3⋊(C23⋊Dic115) |
| unambiguous semidirect product | C23⋊Dic345 |
| derived, Hall | C3×C5×C232 ⋊ C4 |
| Hall | C5×C232 ⋊ Dic3 |
| Hall | C3×C232 ⋊ Dic5 |
| Sylow | C232 ⋊ Dic15 |
| Hall | C3×C5 ⋊ C23⋊Dic23 |
| Sylow | C5 ⋊ C3⋊(C23⋊Dic23) |
| Sylow | C3 ⋊ C23⋊Dic115 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C3⋊(C5⋊(C23⋊D23)) |
| commutator, hypocenter | C3×C5×C232 | C4 |
| Fitting, socle, prime radical, cosocle | C2×C3×C5×C232 | C2 |
| LCS | G ▷ C3×C5×C232 | |
| UCS | C1 ◁ C2 | |
312 conjugacy classes of subgroups.
| transitive degree | μt(G) = 31740 |
Polycyclic presentation:
2,3,5,23^2,2|a^2=f,b^a=b^2,c^a=c^4,d^a=d^22,e^a=e^227938 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31740, 36);