Finite Group DatabasebetaFinite Group Databasebeta| order | 15678 |
| isoclinism | isoclinic class of D117 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C67 · Schur multiplier (H2) = C1 |
| direct product | C67×D117 |
| unambiguous semidirect product | C9⋊(D13×C67) |
| unambiguous semidirect product | C13⋊(D9×C67) |
| Fitting, Hall | C9×C13×C67 ⋊ C2 |
| derived, Hall | C9×C13 ⋊ C2×C67 |
| Hall | C13×C67 ⋊ D9 |
| Hall | C9×C67 ⋊ D13 |
| Sylow | C13 ⋊ D9×C67 |
| Sylow | C9 ⋊ D13×C67 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C67 | D117 |
| commutator, cosocle, hypocenter | C9×C13 | C2×C67 |
| Frattini | C3 | C67×D39 |
| Fitting | C9×C13×C67 | C2 |
| socle | C3×C13×C67 | D3 |
| LCS | G ▷ C9×C13 | |
| UCS | C1 ◁ C67 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7839 |
4020 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D67×D117, D9×D13×C67, D117⋊D67, … |
| maximal normal subgroup of | D67×D117, D9×D13×C67, D117⋊D67, … |
| maximal quotient of | C67×Dic117, C2×C67×D117 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15678, 11);