Finite Group DatabasebetaFinite Group Databasebeta| order | 15730 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C11 |
| unambiguous semidirect product | C5⋊(C11⋊D143) |
| unambiguous semidirect product | C11⋊D715 |
| unambiguous semidirect product | C13⋊(C5⋊(C11⋊D11)) |
| Fitting, socle, derived, Hall | C5×C112×C13 ⋊ C2 |
| Hall | C112×C13 ⋊ D5 |
| Hall | C5×C112 ⋊ D13 |
| Sylow | C112 ⋊ D65 |
| Hall | C5×C13 ⋊ C11⋊D11 |
| Sylow | C13 ⋊ C5⋊(C11⋊D11) |
| Sylow | C5 ⋊ C11⋊D143 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C112×C13 | C2 |
| LCS | G ▷ C5×C112×C13 | |
| UCS | C1 | |
112 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7865 |
Polycyclic presentation:
2,5,11^2,13|b^a=b^4,c^a=c^10,d^a=d^10,e^a=e^123934 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44538241, #44538242, D11×D715, … |
| maximal normal subgroup of | #44538241, #44538242, D11×D715, … |
| maximal quotient of | C11⋊Dic715, C2×C5⋊(C11⋊D143) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15730, 44);