Finite Group DatabasebetaFinite Group Databasebeta| order | 10494 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊D1749 |
| unambiguous semidirect product | C11⋊(C3⋊D159) |
| unambiguous semidirect product | C53⋊(C3⋊D33) |
| Fitting, socle, derived, Hall | C32×C11×C53 ⋊ C2 |
| Hall | C11×C53 ⋊ C3⋊D3 |
| Hall | C32×C53 ⋊ D11 |
| Hall | C32×C11 ⋊ D53 |
| Sylow | C53 ⋊ C3⋊D33 |
| Sylow | C11 ⋊ C3⋊D159 |
| Sylow | C32 ⋊ D583 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C32×C11×C53 | C2 |
| LCS | G ▷ C32×C11×C53 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
Polycyclic presentation:
2,3^2,11,53|b^a=b^2,c^a=c^2,d^a=d^10,e^a=e^522625 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×D1749, D33×D159, D53×C3⋊D33, … |
| maximal normal subgroup of | D3×D1749, D33×D159, D53×C3⋊D33, … |
| maximal quotient of | C3⋊Dic1749, C2×C3⋊D1749 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10494, 10);