Finite Group DatabasebetaFinite Group Databasebeta| order | 15870 |
| isoclinism | isoclinic class of D23 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5×C23 · Schur multiplier (H2) = C1 |
| direct product | C3×C5×C23×D23 |
| unambiguous semidirect product | C23⋊(C2×C3×C5×C23) |
| Fitting, socle, Hall | C3×C5×C232 ⋊ C2 |
| derived | C23 ⋊ C2×C3×C5×C23 |
| Hall | C5×C232 ⋊ C2×C3 |
| Hall | C3×C232 ⋊ C2×C5 |
| Sylow | C232 ⋊ C2×C3×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C5×C23 | D23 |
| commutator, cosocle, hypocenter | C23 | C2×C3×C5×C23 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C232 | C2 |
| LCS | G ▷ C23 | |
| UCS | C1 ◁ C3×C5×C23 | |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 690 |
4485 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C5×D232, C3×D5×C23×D23, C3×D23×D115, … |
| maximal normal subgroup of | C3×C5×D232, C3×D5×C23×D23, C3×D23×D115, … |
| maximal quotient of | C3×C5×C23×Dic23, C2×C3×C5×C23×D23 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15870, 26);