Finite Group DatabasebetaFinite Group Databasebeta| order | 15678 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C13 · Schur multiplier (H2) = C1 |
| direct product | C13×C3⋊(D67⋊C3) |
| unambiguous semidirect product | C3⋊(C13×D67⋊C3) |
| unambiguous semidirect product | (C67⋊C3)⋊(D3×C13) |
| unambiguous semidirect product | D201⋊(C3×C13) |
| Fitting, socle | C3×C13×C67 ⋊ C2×C3 |
| derived | C3×C67 ⋊ C2×C3×C13 |
| Hall | C3×C13×C67⋊C3 ⋊ C2 |
| Hall | C13×C67 ⋊ C3×D3 |
| Hall | C3×C67⋊C3 ⋊ C2×C13 |
| Sylow | C67 ⋊ C3×D3×C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13 | C3⋊(D67⋊C3) |
| commutator, cosocle, hypocenter | C3×C67 | C2×C3×C13 |
| Frattini | C1 | G |
| Fitting, socle | C3×C13×C67 | C2×C3 |
| LCS | G ▷ C3×C67 | |
| UCS | C1 ◁ C13 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2613 |
546 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15678, 42);