Finite Group DatabasebetaFinite Group Databasebeta| order | 5060 |
| automorphism | Aut(G) order 2226400 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| dihedral | D2530 |
| direct product | C2×D1265 |
| unambiguous semidirect product | (C2×C5)⋊D253 |
| unambiguous semidirect product | (C2×C11)⋊D115 |
| unambiguous semidirect product | (C2×C23)⋊D55 |
| Fitting, socle | C2×C5×C11×C23 ⋊ C2 |
| derived, Hall | C5×C11×C23 ⋊ C22 |
| Hall | C11×C23 ⋊ C2×D5 |
| Hall | C5×C23 ⋊ C2×D11 |
| Hall | C5×C11 ⋊ C2×D23 |
| Sylow | C23 ⋊ C2×D55 |
| Sylow | C11 ⋊ C2×D115 |
| Sylow | C5 ⋊ C2×D253 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D1265 |
| commutator, hypocenter | C5×C11×C23 | C22 |
| Frattini | C1 | G |
| Fitting, socle | C2×C5×C11×C23 | C2 |
| LCS | G ▷ C5×C11×C23 | |
| UCS | C1 ◁ C2 | |
40 conjugacy classes of subgroups.
1268 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×D1265, C2×D3795, C2×C3×D1265, … |
| maximal normal subgroup of | C2×C3×D1265, C2×C5⋊(C23⋊AGL(1,𝔽11)), C2×C5×D1265, … |
| maximal quotient of | D3×D1265, C2×D3795, C2×C3×D1265, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5060, 41);