Finite Group DatabasebetaFinite Group Databasebeta| order | 15730 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C13 · Schur multiplier (H2) = C1 |
| direct product | C2×C13×C121⋊C5 |
| unambiguous semidirect product | (C2×C121)⋊(C5×C13) |
| unambiguous semidirect product | (C2×C13×C121)⋊C5 |
| Fitting, Hall | C2×C13×C121 ⋊ C5 |
| derived, Sylow | C121 ⋊ C2×C5×C13 |
| Hall | C13×C121 ⋊ C2×C5 |
| Hall | C2×C121 ⋊ C5×C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C13 | C121⋊C5 |
| commutator, cosocle, hypocenter | C121 | C2×C5×C13 |
| Frattini | C11 | C2×C13×C11⋊C5 |
| Fitting | C2×C13×C121 | C5 |
| socle | C2×C11×C13 | C11⋊C5 |
| LCS | G ▷ C121 | |
| UCS | C1 ◁ C2×C13 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3146 |
754 conjugacy classes. The character table is too large to display.
| maximal subgroup of | Dic13×C121⋊C5, C13×Dic121⋊C5, (C121⋊C5)⋊Dic13, … |
| maximal normal subgroup of | Dic13×C121⋊C5, C13×Dic121⋊C5, (C121⋊C5)⋊Dic13, … |
| maximal quotient of | C4×C13×C121⋊C5, C22×C13×C121⋊C5 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15730, 5);