Finite Group DatabasebetaFinite Group Databasebeta| order | 10780 |
| automorphism | Aut(G) order 9055200 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| dihedral | D5390 |
| direct product | C2×D2695 |
| unambiguous semidirect product | (C2×C5)⋊D539 |
| unambiguous semidirect product | (C2×C11)⋊D245 |
| unambiguous semidirect product | (C2×C49)⋊D55 |
| Fitting | C2×C5×C11×C49 ⋊ C2 |
| derived, Hall | C5×C11×C49 ⋊ C22 |
| Hall | C11×C49 ⋊ C2×D5 |
| Hall | C5×C49 ⋊ C2×D11 |
| Hall | C5×C11 ⋊ C2×D49 |
| Sylow | C49 ⋊ C2×D55 |
| Sylow | C11 ⋊ C2×D245 |
| Sylow | C5 ⋊ C2×D539 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D2695 |
| commutator, cosocle, hypocenter | C5×C11×C49 | C22 |
| Frattini | C7 | C2×D385 |
| Fitting | C2×C5×C11×C49 | C2 |
| socle | C2×C5×C7×C11 | D7 |
| LCS | G ▷ C5×C11×C49 | |
| UCS | C1 ◁ C2 | |
60 conjugacy classes of subgroups.
2698 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C5⋊(C11⋊(D49⋊C3)), D3×D2695, C2×C3×D2695, … |
| maximal normal subgroup of | C2×C5⋊(C11⋊(D49⋊C3)), C2×C3×D2695, D10780 |
| maximal quotient of | D3×D2695, C2×C3×D2695, C2×D8085, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10780, 36);