Finite Group DatabasebetaFinite Group Databasebeta| order | 15730 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C13⋊(D121⋊C5) |
| unambiguous semidirect product | (C121⋊C5)⋊D13 |
| unambiguous semidirect product | D1573⋊C5 |
| Fitting, derived, Hall | C13×C121 ⋊ C2×C5 |
| Hall | C13×C121⋊C5 ⋊ C2 |
| Hall | D1573 ⋊ C5 |
| Hall | C121⋊C5 ⋊ D13 |
| Sylow | C121 ⋊ C5×D13 |
| Sylow | C13 ⋊ D121⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C13×C121 | C2×C5 |
| Frattini | C11 | C13⋊AGL(1,𝔽11) |
| socle | C11×C13 | AGL(1,𝔽11) |
| LCS | G ▷ C13×C121 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1573 |
Polycyclic presentation:
2,5,11,13,11|c^11=e^10,c^a=c^10e,d^a=d^12,e^a=e^10,c^b=c^4e^4,e^b=e^4196 conjugacy classes — view the full character table.
| maximal subgroup of | D13×D121⋊C5, C2×C13⋊(D121⋊C5) |
| maximal normal subgroup of | D13×D121⋊C5, C2×C13⋊(D121⋊C5) |
| maximal quotient of | (C121⋊C5)⋊Dic13, C2×C13⋊(D121⋊C5) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15730, 4);