Finite Group DatabasebetaFinite Group Databasebeta| order | 15870 |
| isoclinism | isoclinic class of D15 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C232 · Schur multiplier (H2) = C23 |
| direct product | C232×D15 |
| unambiguous semidirect product | C3⋊(D5×C232) |
| unambiguous semidirect product | C5⋊(D3×C232) |
| Fitting, socle, Hall | C3×C5×C232 ⋊ C2 |
| derived, Hall | C3×C5 ⋊ C2×C232 |
| Hall | C5×C232 ⋊ D3 |
| Hall | C3×C232 ⋊ D5 |
| Sylow | C5 ⋊ D3×C232 |
| Sylow | C3 ⋊ D5×C232 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C232 | D15 |
| commutator, cosocle, hypocenter | C3×C5 | C2×C232 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C232 | C2 |
| LCS | G ▷ C3×C5 | |
| UCS | C1 ◁ C232 | |
208 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7935 |
4761 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C23×D15×D23, D15×C23⋊D23, D3×D5×C232, … |
| maximal normal subgroup of | C23×D15×D23, D15×C23⋊D23, D3×D5×C232, … |
| maximal quotient of | C232×Dic15, C2×C232×D15 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15870, 18);