Finite Group DatabasebetaFinite Group Databasebeta| order | 15730 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| direct product | D13×C121⋊C5 |
| unambiguous semidirect product | C13⋊(C2×C121⋊C5) |
| unambiguous semidirect product | (D13×C121)⋊C5 |
| Fitting, derived, Hall | C13×C121 ⋊ C2×C5 |
| Hall | C13×C121⋊C5 ⋊ C2 |
| Hall | D13×C121 ⋊ C5 |
| Sylow | C121 ⋊ C5×D13 |
| Sylow | C13 ⋊ C2×C121⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C13×C121 | C2×C5 |
| Frattini | C11 | D13×C11⋊C5 |
| socle | C11×C13 | C2×C11⋊C5 |
| LCS | G ▷ C13×C121 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1573 |
232 conjugacy classes — view the full character table.
| maximal subgroup of | (C121⋊C5)⋊#261, D13×D121⋊C5, #261×C121⋊C5, … |
| maximal normal subgroup of | (C121⋊C5)⋊#261, D13×D121⋊C5, #261×C121⋊C5, … |
| maximal quotient of | Dic13×C121⋊C5, C2×D13×C121⋊C5 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15730, 2);