Finite Group DatabasebetaFinite Group Databasebeta| order | 5060 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D23×D55 |
| unambiguous semidirect product | (C5×D23)⋊D11 |
| unambiguous semidirect product | (C11×D23)⋊D5 |
| Fitting, socle, 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 ⋊ D5×D23 |
| Sylow | C5 ⋊ D11×D23 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C11×C23 | C22 |
| LCS | G ▷ C5×C11×C23 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
377 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D23×D55, D23×D165, D55×D69, … |
| maximal normal subgroup of | C3×D23×D55, D23×C5⋊AGL(1,𝔽11), C5×D23×D55, … |
| maximal quotient of | C3×D23×D55, D23×D165, D55×D69, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5060, 36);