Finite Group DatabasebetaFinite Group Databasebeta| order | 15730 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C13⋊#11925895 |
| Fitting, socle, derived, Hall | C112×C13 ⋊ C2×C5 |
| Hall | C13×#10597243 ⋊ C2 |
| Hall | C11×D143 ⋊ C5 |
| Hall | #10597243 ⋊ D13 |
| Sylow | C112 ⋊ C5×D13 |
| Sylow | C13 ⋊ #11925895 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C112×C13 | C2×C5 |
| LCS | G ▷ C112×C13 | |
| UCS | C1 | |
52 conjugacy classes of subgroups.
| transitive degree | μt(G) = 286 |
Polycyclic presentation:
2,5,11^2,13|c^a=c^10,e^a=e^12,c^b=c^4,d^b=d^4199 conjugacy classes — view the full character table.
| maximal subgroup of | D13×#11925895, #11925895⋊D13, #11925892⋊D13, … |
| maximal normal subgroup of | D13×#11925895, #11925895⋊D13, #11925892⋊D13, … |
| maximal quotient of | #44538118, C2×C13⋊#11925895 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15730, 24);