Finite Group DatabasebetaFinite Group Databasebeta| order | 15870 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | C3⋊(C5⋊(C23⋊D23)) |
| unambiguous semidirect product | C5⋊(C3⋊(C23⋊D23)) |
| unambiguous semidirect product | C23⋊D345 |
| Fitting, socle, derived, Hall | C3×C5×C232 ⋊ C2 |
| Hall | C5×C232 ⋊ D3 |
| Hall | C3×C232 ⋊ D5 |
| Sylow | C232 ⋊ D15 |
| Hall | C3×C5 ⋊ C23⋊D23 |
| Sylow | C5 ⋊ C3⋊(C23⋊D23) |
| Sylow | C3 ⋊ C5⋊(C23⋊D23) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C5×C232 | C2 |
| LCS | G ▷ C3×C5×C232 | |
| UCS | C1 | |
208 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7935 |
Polycyclic presentation:
2,3,5,23^2|b^a=b^2,c^a=c^4,d^a=d^22,e^a=e^223969 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D23×D345, D15×C23⋊D23, D69×D115, … |
| maximal normal subgroup of | D23×D345, D15×C23⋊D23, D69×D115, … |
| maximal quotient of | C3⋊(C23⋊Dic115), C2×C3⋊(C5⋊(C23⋊D23)) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15870, 16);