Finite Group DatabasebetaFinite Group Databasebeta| order | 15314 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C19 · Schur multiplier (H2) = C1 |
| direct product | C19×D403 |
| unambiguous semidirect product | C13⋊(C19×D31) |
| unambiguous semidirect product | C31⋊(C19×D13) |
| Fitting, socle, Hall | C13×C19×C31 ⋊ C2 |
| derived, Hall | C13×C31 ⋊ C2×C19 |
| Hall | C19×C31 ⋊ D13 |
| Hall | C13×C19 ⋊ D31 |
| Sylow | C31 ⋊ C19×D13 |
| Sylow | C13 ⋊ C19×D31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C19 | D403 |
| commutator, cosocle, hypocenter | C13×C31 | C2×C19 |
| Frattini | C1 | G |
| Fitting, socle | C13×C19×C31 | C2 |
| LCS | G ▷ C13×C31 | |
| UCS | C1 ◁ C19 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7657 |
3857 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C19×D13×D31, D19×D403, D247⋊D31, … |
| maximal normal subgroup of | C19×D13×D31, D19×D403, D247⋊D31, … |
| maximal quotient of | C19×Dic403, C2×C19×D403 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15314, 6);