Finite Group DatabasebetaFinite Group Databasebeta| order | 15730 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C11 |
| direct product | D13×#10597245 |
| unambiguous semidirect product | C13⋊(C2×#10597245) |
| Fitting, socle, derived, Hall | C112×C13 ⋊ C2×C5 |
| Hall | C13×#10597245 ⋊ C2 |
| Hall | C112×D13 ⋊ C5 |
| Sylow | C112 ⋊ C5×D13 |
| Sylow | C13 ⋊ C2×#10597245 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C112×C13 | C2×C5 |
| LCS | G ▷ C112×C13 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 715 |
232 conjugacy classes — view the full character table.
| maximal subgroup of | #44538150, D13×#11925890, #44538191, … |
| maximal normal subgroup of | #44538150, D13×#11925890, #44538191, … |
| maximal quotient of | Dic13×#10597245, C2×D13×#10597245 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15730, 34);