Finite Group DatabasebetaFinite Group Databasebeta| order | 15730 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C11 |
| direct product | C5×C11⋊D143 |
| unambiguous semidirect product | C13⋊(C5×C11⋊D11) |
| Fitting, socle, Hall | C5×C112×C13 ⋊ C2 |
| derived, Hall | C112×C13 ⋊ C2×C5 |
| Hall | C5×C112 ⋊ D13 |
| Sylow | C112 ⋊ C5×D13 |
| Hall | C5×C13 ⋊ C11⋊D11 |
| Sylow | C13 ⋊ C5×C11⋊D11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | C11⋊D143 |
| commutator, cosocle, hypocenter | C112×C13 | C2×C5 |
| Frattini | C1 | G |
| Fitting, socle | C5×C112×C13 | C2 |
| LCS | G ▷ C112×C13 | |
| UCS | C1 ◁ C5 | |
112 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7865 |
3940 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×#20262573, C5×D11×D143, C5×D13×C11⋊D11, … |
| maximal normal subgroup of | C5×#20262573, C5×D11×D143, C5×D13×C11⋊D11, … |
| maximal quotient of | C5×C11⋊Dic143, C2×C5×C11⋊D143 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15730, 50);