Finite Group DatabasebetaFinite Group Databasebeta| order | 7524 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C3 |
| direct product | C3⋊D3×D209 |
| Fitting, socle, derived, Hall | C32×C11×C19 ⋊ C22 |
| Hall | C11×C19 ⋊ C2×C3⋊D3 |
| Hall | C32×C19 ⋊ C2×D11 |
| Hall | C32×C11 ⋊ C2×D19 |
| Sylow | C19 ⋊ C3⋊D3×D11 |
| Sylow | C11 ⋊ C3⋊D3×D19 |
| Sylow | C32 ⋊ C2×D209 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C32×C11×C19 | C22 |
| LCS | G ▷ C32×C11×C19 | |
| UCS | C1 | |
120 conjugacy classes of subgroups.
636 conjugacy classes — view the full character table.
| maximal subgroup of | C3⋊D3×C19⋊AGL(1,𝔽11), C5×C3⋊D3×D209, C3⋊D15×D209, … |
| maximal normal subgroup of | C3⋊D3×C19⋊AGL(1,𝔽11), C5×C3⋊D3×D209 |
| maximal quotient of | C5×C3⋊D3×D209, C3⋊D15×D209, C3⋊D3×D1045, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7524, 92);