Finite Group DatabasebetaFinite Group Databasebeta| order | 10780 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D55⋊D49 |
| unambiguous semidirect product | D245⋊D11 |
| unambiguous semidirect product | D539⋊D5 |
| Fitting, derived, Hall | C5×C11×C49 ⋊ C22 |
| Hall | C11×C49 ⋊ C2×D5 |
| Hall | C5×C49 ⋊ C2×D11 |
| Hall | C5×C11 ⋊ C2×D49 |
| Sylow | C49 ⋊ D5×D11 |
| Sylow | C11 ⋊ D5×D49 |
| Sylow | C5 ⋊ D11×D49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C5×C11×C49 | C22 |
| Frattini | C7 | D35⋊D11 |
| socle | C5×C7×C11 | C2×D7 |
| LCS | G ▷ C5×C11×C49 | |
| UCS | C1 | |
60 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,5,7,11,7|d^7=f^6,d^a=d^6f,e^a=e^10,f^a=f^6,c^b=c^4,d^b=d^6f,f^b=f^6724 conjugacy classes — view the full character table.
| maximal subgroup of | D55⋊(D49⋊C3), C3×D55⋊D49, D539⋊D15, … |
| maximal normal subgroup of | D55⋊(D49⋊C3), C3×D55⋊D49 |
| maximal quotient of | C3×D55⋊D49, D539⋊D15, D55⋊D147, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10780, 29);