Finite Group DatabasebetaFinite Group Databasebeta| order | 15314 |
| isoclinism | isoclinic class of D247 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C31 · Schur multiplier (H2) = C1 |
| direct product | C31×D247 |
| unambiguous semidirect product | C13⋊(C31×D19) |
| unambiguous semidirect product | C19⋊(D13×C31) |
| Fitting, socle, Hall | C13×C19×C31 ⋊ C2 |
| derived, Hall | C13×C19 ⋊ C2×C31 |
| Hall | C19×C31 ⋊ D13 |
| Hall | C13×C31 ⋊ D19 |
| Sylow | C19 ⋊ D13×C31 |
| Sylow | C13 ⋊ C31×D19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C31 | D247 |
| commutator, cosocle, hypocenter | C13×C19 | C2×C31 |
| Frattini | C1 | G |
| Fitting, socle | C13×C19×C31 | C2 |
| LCS | G ▷ C13×C19 | |
| UCS | C1 ◁ C31 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7657 |
3875 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D31×D247, D13×C31×D19, D247⋊D31, … |
| maximal normal subgroup of | D31×D247, D13×C31×D19, D247⋊D31, … |
| maximal quotient of | C31×Dic247, C2×C31×D247 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15314, 7);