Finite Group DatabasebetaFinite Group Databasebeta| order | 5588 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D11×D127 |
| unambiguous semidirect product | (D11×C127)⋊C2 |
| unambiguous semidirect product | (C11×D127)⋊C2 |
| unambiguous semidirect product | D1397⋊C2 |
| Fitting, socle, derived, Hall | C11×C127 ⋊ C22 |
| Sylow | C127 ⋊ C2×D11 |
| Sylow | C11 ⋊ C2×D127 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C11×C127 | C22 |
| LCS | G ▷ C11×C127 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
455 conjugacy classes — view the full character table.
| maximal subgroup of | D11×D127⋊C3, C3×D11×D127, D33×D127, … |
| maximal normal subgroup of | D11×D127⋊C3, C3×D11×D127, AGL(1,𝔽11)×D127, … |
| maximal quotient of | C3×D11×D127, D33×D127, D11×D381, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5588, 6);