Finite Group DatabasebetaFinite Group Databasebeta| order | 15730 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C13 · Schur multiplier (H2) = C11 |
| direct product | C13×C5⋊(C11⋊D11) |
| unambiguous semidirect product | C5⋊(C13×C11⋊D11) |
| unambiguous semidirect product | C11⋊(C13×D55) |
| Fitting, socle, Hall | C5×C112×C13 ⋊ C2 |
| derived, Hall | C5×C112 ⋊ C2×C13 |
| Hall | C112×C13 ⋊ D5 |
| Sylow | C112 ⋊ D5×C13 |
| Hall | C5×C13 ⋊ C11⋊D11 |
| Sylow | C5 ⋊ C13×C11⋊D11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13 | C5⋊(C11⋊D11) |
| commutator, cosocle, hypocenter | C5×C112 | C2×C13 |
| Frattini | C1 | G |
| Fitting, socle | C5×C112×C13 | C2 |
| LCS | G ▷ C5×C112 | |
| UCS | C1 ◁ C13 | |
112 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7865 |
3952 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C13×#14559097, #44538243, C13×D11×D55, … |
| maximal normal subgroup of | C13×#14559097, #44538243, C13×D11×D55, … |
| maximal quotient of | C13×C11⋊Dic55, C2×C13×C5⋊(C11⋊D11) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15730, 45);