Finite Group DatabasebetaFinite Group Databasebeta| order | 15730 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C13⋊#11925890 |
| Fitting, socle, Hall | C112×C13 ⋊ D5 |
| derived, Hall | C13×#10597245 ⋊ C2 |
| Hall | #10597245 ⋊ D13 |
| Sylow | C112 ⋊ D65 |
| Sylow | C13 ⋊ #11925890 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C13×#10597245 | C2 |
| Fitting, socle | C112×C13 | D5 |
| LCS | G ▷ C13×#10597245 | |
| UCS | C1 | |
28 conjugacy classes of subgroups.
| transitive degree | μt(G) = 286 |
Polycyclic presentation:
2,5,13,11^2|b^a=b^4,c^a=c^12,d^a=d^3e^3,e^a=de^8,d^b=d^4e^8,e^b=e^3205 conjugacy classes — view the full character table.
| maximal subgroup of | D13×#11925890, #11925890⋊D13, #44538160, … |
| maximal normal subgroup of | D13×#11925890, #11925890⋊D13, #44538160, … |
| maximal quotient of | #44538133, C2×C13⋊#11925890 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15730, 39);