Finite Group DatabasebetaFinite Group Databasebeta| order | 7436 |
| automorphism | Aut(G) order 5800080 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| dihedral | D3718 |
| direct product | C2×D1859 |
| unambiguous semidirect product | (C2×C11)⋊D169 |
| unambiguous semidirect product | (C2×C169)⋊D11 |
| Fitting | C2×C11×C169 ⋊ C2 |
| derived, Hall | C11×C169 ⋊ C22 |
| Sylow | C169 ⋊ C2×D11 |
| Sylow | C11 ⋊ C2×D169 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D1859 |
| commutator, hypocenter | C11×C169 | C22 |
| Frattini | C13 | C2×D143 |
| Fitting | C2×C11×C169 | C2 |
| socle | C2×C11×C13 | D13 |
| LCS | G ▷ C11×C169 | |
| UCS | C1 ◁ C2 | |
30 conjugacy classes of subgroups.
1862 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C11⋊(D169⋊C3), D3×D1859, C2×C3×D1859, … |
| maximal normal subgroup of | C2×C11⋊(D169⋊C3), C2×C3×D1859, C2×(C11⋊C5)⋊D169, … |
| maximal quotient of | D3×D1859, C2×C3×D1859, C2×D5577, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7436, 11);