Finite Group DatabasebetaFinite Group Databasebeta| order | 10780 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×Dic245 |
| unambiguous semidirect product | C49⋊(C11×Dic5) |
| derived, Hall | C5×C49 ⋊ C4×C11 |
| Hall | C5×C11×C49 ⋊ C4 |
| Hall | C11×C49 ⋊ Dic5 |
| Hall | C5×C11 ⋊ Dic49 |
| Sylow | C49 ⋊ C11×Dic5 |
| Sylow | C5 ⋊ C11×Dic49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C11 | D245 |
| commutator, hypocenter | C5×C49 | C4×C11 |
| Frattini | C2×C7 | C11×D35 |
| Fitting | C2×C5×C11×C49 | C2 |
| socle, prime radical | C2×C5×C7×C11 | D7 |
| cosocle | C2×C5×C49 | C2×C11 |
| LCS | G ▷ C5×C49 | |
| UCS | C1 ◁ C2×C11 | |
36 conjugacy classes of subgroups.
2728 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C11×Dic245, C11×Dic735, C11×(C49⋊C3)⋊Dic5 |
| maximal normal subgroup of | C3×C11×Dic245, C11×(C49⋊C3)⋊Dic5 |
| maximal quotient of | C3×C11×Dic245, C11×Dic735 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10780, 11);