Finite Group DatabasebetaFinite Group Databasebeta| order | 5148 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D3×D429 |
| unambiguous semidirect product | (C3×D3)⋊D143 |
| unambiguous semidirect product | (D3×C11)⋊D39 |
| unambiguous semidirect product | (D3×C13)⋊D33 |
| Fitting, socle, derived, Hall | C32×C11×C13 ⋊ C22 |
| Hall | C11×C13 ⋊ D32 |
| Hall | C32×C13 ⋊ C2×D11 |
| Hall | C32×C11 ⋊ C2×D13 |
| Sylow | C13 ⋊ D3×D33 |
| Sylow | C11 ⋊ D3×D39 |
| Sylow | C32 ⋊ C2×D143 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C32×C11×C13 | C22 |
| LCS | G ▷ C32×C11×C13 | |
| UCS | C1 | |
88 conjugacy classes of subgroups.
648 conjugacy classes — view the full character table.
| maximal subgroup of | D3×C3⋊(C13⋊AGL(1,𝔽11)), C5×D3×D429, D3×D2145, … |
| maximal normal subgroup of | D3×C3⋊(C13⋊AGL(1,𝔽11)), C5×D3×D429, D3×C7×D429 |
| maximal quotient of | C5×D3×D429, D3×D2145, D15×D429, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5148, 104);