Finite Group DatabasebetaFinite Group Databasebeta| order | 15678 |
| isoclinism | isoclinic class of C3⋊D39 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C67 · Schur multiplier (H2) = C3 |
| direct product | C67×C3⋊D39 |
| unambiguous semidirect product | C3⋊(C67×D39) |
| unambiguous semidirect product | C13⋊(C3⋊D3×C67) |
| Fitting, socle, Hall | C32×C13×C67 ⋊ C2 |
| derived, Hall | C32×C13 ⋊ C2×C67 |
| Hall | C13×C67 ⋊ C3⋊D3 |
| Hall | C32×C67 ⋊ D13 |
| Sylow | C13 ⋊ C3⋊D3×C67 |
| Sylow | C32 ⋊ D13×C67 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C67 | C3⋊D39 |
| commutator, cosocle, hypocenter | C32×C13 | C2×C67 |
| Frattini | C1 | G |
| Fitting, socle | C32×C13×C67 | C2 |
| LCS | G ▷ C32×C13 | |
| UCS | C1 ◁ C67 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7839 |
4020 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C67×#90866, C67⋊#90866, D3×C67×D39, … |
| maximal normal subgroup of | C67×#90866, C67⋊#90866, D3×C67×D39, … |
| maximal quotient of | C67×C3⋊Dic39, C2×C67×C3⋊D39 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15678, 63);