Finite Group DatabasebetaFinite Group Databasebeta| order | 5124 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D7×D183 |
| unambiguous semidirect product | (C3×D7)⋊D61 |
| unambiguous semidirect product | (D7×C61)⋊D3 |
| Fitting, socle, derived, Hall | C3×C7×C61 ⋊ C22 |
| Hall | C7×C61 ⋊ C2×D3 |
| Hall | C3×C61 ⋊ C2×D7 |
| Sylow | C61 ⋊ D3×D7 |
| Hall | C3×C7 ⋊ C2×D61 |
| Sylow | C7 ⋊ C2×D183 |
| Sylow | C3 ⋊ D7×D61 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C7×C61 | C22 |
| LCS | G ▷ C3×C7×C61 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
465 conjugacy classes — view the full character table.
| maximal subgroup of | D7×D549, #14579425⋊D3, #14579424⋊D3, … |
| maximal normal subgroup of | #14579425⋊D3, #14579424⋊D3, AGL(1,𝔽7)×D183, … |
| maximal quotient of | D7×D549, C3×D7×D183, D7×C3⋊D183, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5124, 58);