Finite Group DatabasebetaFinite Group Databasebeta| order | 17622 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊D2937 |
| unambiguous semidirect product | C11⋊(C3⋊D267) |
| unambiguous semidirect product | C89⋊(C3⋊D33) |
| Fitting, socle, derived, Hall | C32×C11×C89 ⋊ C2 |
| Hall | C11×C89 ⋊ C3⋊D3 |
| Hall | C32×C89 ⋊ D11 |
| Hall | C32×C11 ⋊ D89 |
| Sylow | C89 ⋊ C3⋊D33 |
| Sylow | C11 ⋊ C3⋊D267 |
| Sylow | C32 ⋊ D979 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C32×C11×C89 | C2 |
| LCS | G ▷ C32×C11×C89 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8811 |
Polycyclic presentation:
2,3^2,11,89|b^a=b^2,c^a=c^2,d^a=d^10,e^a=e^884407 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×D2937, D33×D267, D89×C3⋊D33, … |
| maximal normal subgroup of | D3×D2937, D33×D267, D89×C3⋊D33, … |
| maximal quotient of | C3⋊Dic2937, C2×C3⋊D2937 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17622, 20);