Finite Group DatabasebetaFinite Group Databasebeta| order | 15642 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊D2607 |
| unambiguous semidirect product | C11⋊(C3⋊D237) |
| unambiguous semidirect product | C79⋊(C3⋊D33) |
| Fitting, socle, derived, Hall | C32×C11×C79 ⋊ C2 |
| Hall | C11×C79 ⋊ C3⋊D3 |
| Hall | C32×C79 ⋊ D11 |
| Hall | C32×C11 ⋊ D79 |
| Sylow | C79 ⋊ C3⋊D33 |
| Sylow | C11 ⋊ C3⋊D237 |
| Sylow | C32 ⋊ D869 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C32×C11×C79 | C2 |
| LCS | G ▷ C32×C11×C79 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7821 |
Polycyclic presentation:
2,3^2,11,79|b^a=b^2,c^a=c^2,d^a=d^10,e^a=e^783912 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×D2607, D33×D237, D79×C3⋊D33, … |
| maximal normal subgroup of | D3×D2607, D33×D237, D79×C3⋊D33, … |
| maximal quotient of | C3⋊Dic2607, C2×C3⋊D2607 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15642, 22);